- Catalog Entry
- Nickname: IntAlgwP
- Credits: 5
- Grades: A-F
- Description: Developmental course in algebra for students in need of preparation for math placement level PL1. Operations and equations with rational expressions, equations of a line, introduction to functions, introduction to systems of linear equations in two and three variables, absolute-value equations and inequalities, rational exponents, operations and equations with radicals, introduction to complex numbers, quadratic equations and various application problems on these topics. Same as Math D005, but with more review of basic pre-algebra material. Students cannot earn credit for both MATH D005 and D004.
- Prerequisites: PL DV
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 102
- Sample textbook: Intermediate Algebra, R. Larson 5th edition.
- Topics:
- Review of arithmetic operations with whole numbers, integers, fractions, and decimal numbers
- Operations and equations with polynomials
- Operations and equations with rational expressions
- Linear equations and Linear inequalities in one unknown and their solution
- Introduction to Functions
- Introduction to systems of linear equations in two and three variables
- Absolute-value equations and inequalities
- Rational exponents, operations and equations with radicals
- Introduction to complex numbers
- Quadratic equations, factoring and the quadratic formula
- Various application problems on these topics

- Desired learning outcomes (ability to...):
- Perform operations on real numbers
- Understand basic arithmetical operations, fractions and decimals
- Simplify algebraic and exponential expressions
- Solve linear equations and inequalities
- Graph linear and other functions
- Add, multiply and factor polynomials
- Add, multiply, divide and simplify rational expressions
- Solve linear systems of equations with 2 and 3 variables
- Solve equations and inequalities with absolute values
- Evaluate formulas using algebraic substitutions
- Manipulate rational exponents and radicals in functions and equations
- Add and multiply complex numbers
- Solve quadratic equations using the quadratic formula, including all cases
- Apply algebraic operations in the context of problem solving

- Cluster: Lower Undergraduate

- Catalog Entry
- Abbreviated Title: Intermediate Algebra
- Nickname: IntAlg
- Credits: 4
- Grades: A-F
- Description: Developmental course in algebra for students in need of preparation for math placement level PL1. Operations and equations with rational expressions, equations of a line, introduction to functions, introduction to systems of linear equations in two and three variables, absolute-value equations and inequalities, rational exponents, operations and equations with radicals, introduction to complex numbers, quadratic equations and various application problems on these topics. Students cannot earn credit for both MATH D005 and D004.
- Prerequisites: PL DV
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 102
- Sample textbook: Intermediate Algebra, R. Larson 5th edition.
- Topics:
- Operations and equations with polynomials
- Operations and equations with rational expressions
- Linear equations and Linear inequalities in one unknown and their solution
- Introduction to Functions
- Introduction to systems of linear equations in two and three variables
- Absolute-value equations and inequalities
- Rational exponents, operations and equations with radicals
- Introduction to complex numbers
- Quadratic equations, factoring and the quadratic formula
- Various application problems on these topics

- Desired learning outcomes (ability to...):
- Simplify algebraic and exponential expressions
- Solve linear equations and inequalities
- Graph linear and other functions
- Add, multiply and factor polynomials
- Add, multiply, divide and simplify rational expressions
- Solve linear systems of equations with 2 and 3 variables
- Solve equations and inequalities with absolute values
- Evaluate formulas using algebraic substitutions
- Manipulate rational exponents and radicals in functions and equations
- Add and multiply complex numbers
- Solve quadratic equations using the quadratic formula, including all cases
- Apply algebraic operations in the context of problem solving

- Cluster: Lower Undergraduate

- Catalog Entry
- Abbreviated Title: PLTL for PreCalculus
- Credits: 1
- Grades: F, CR
- Description: Small groups of students concurrently enrolled in MATH 1300 meet in weekly workshops with a peer mentor. Together, they work on problem sets, reading and team-based learning projects to master the material in MATH 1300 and the mathematical reasoning it requires..
- Prerequisites: concurrent 1300 Pre-Calculus
- Taught in: Fall, Spring
- Frequency: Sporadically
- Replaces the quarter course: 103P
- Sample textbook: Same as 1300
- Topics:
- Same as PreCalculus

- Desired learning outcomes (ability to...):
- Students can pass PreCalculus

- Catalog Entry
- Abbreviated Title: PLTL for Calculus I
- Credits: 1
- Grades: F, CR
- Description: Small groups of students concurrently enrolled in MATH 2301 meet in weekly workshops with a peer mentor. Together, they work on problem sets, reading and team-based learning projects to master the material in MATH 2301 and the mathematical reasoning it requires..
- Prerequisites: concurrent 2301 Calculus I
- Taught in: Fall, Spring, Summer
- Frequency: Sporadically
- Replaces the quarter course: 103A
- Sample textbook: Same as 2301
- Topics:
- Same as Calculus I

- Desired learning outcomes (ability to...):
- Students can pass Calculus I

- Catalog Entry
- Abbreviated Title: Consumer Math
- Nickname: Consumer
- Credits: 3
- Grades: A-F
- Description: Applications of elementary mathematics to day-to-day problems. Special emphasis on consumer topics such as compound interest, mortgages, and installment buying. Scientific calculator required. Does not apply to arts and sciences requirements. No credit to those with credit for course above MATH 1200.
- Prerequisites: (PL1 or C or T or better in D004 Intermediate Algebra with PreAlgebra or C or T or better in D005 Intermediate Algebra)
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 109 Consumer Math
- Sample textbook: Miller, Salzman, and Clenden, Business Mathematics (10th edition), Addison-Wesley
- Topics:
- Topics focus on consumer mathematics, including:
- Whole numbers and decimal, fractions, and percentages.
- Discounts and Markups in business settings
- Simple and Compound interest; present and future value
- Mortgages and installment buying.

- Desired learning outcomes (ability to...):
- Students can use elementary business mathematics in a variety of applications.

- Cluster: Lower Undergraduate

- Catalog Entry
- Abbreviated Title: Elementary Topics in Math I
- Nickname: ElemTopI
- Credits: 3
- Grades: A-F
- Description: Elementary Topics in Mathematics I&II is a sequence for majors in elementary education and related fields. The course focuses on the development of arithmetic and number systems, including whole numbers, integers, and rational numbers. Probability and data analysis are studied as applications of rational numbers and emphasize mathematical representation and communication. Satisfies Tier I requirement for elementary education majors only. Does not apply to Arts and Sciences natural science requirements.
- Prerequisites: (PL1 or C or T or better in D004 Intermediate Algebra with PreAlgebra or C or T or better in D005 Intermediate Algebra)
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 120, 121 Elementary Topics in Math
- Sample textbook: O'Daffer, P., Charles, R., Cooney, T., Dossey, J., Schielack, J. (2008). Mathematics for Elementary School Teachers (4 ed.). NY: Addison-Wesley.
- Topics:
- 1 Reasoning and Problem Solving, Sets, Whole Numbers, Addition & Subtraction models
- 2 Mult and Div models, Div by zero, Props of add, subt, mult and div, Hindu-Arabic Numeration
- 3 Place value and numeration in other bases, Mental computation and estimation strategies
- 4 Arithmetic algorithms including non-decimal bases, factors and divisibility
- 5 Number theory including GCF, LCM, prime factorization; Integers
- 6 Fractions and rational numbers, addition and subtraction of fractions
- 7 Mult and div of fractions, modelling mult and div, operations with decimals
- 8 Terminating and repeating decimals, scientific notation
- 9 Ratios and proportions
- 10 Percentages, converting decimals to percents to fractions
- 11 Introduction to probability and probability models
- 12 Principles of counting, conditional probability
- 13 Geometric probability, simulations, odds and expected value
- 14 Permutations, Combinations, one- and two-variable Data displays
- 15 Measures of central tendancy and spread, Using data to make decisions

- Desired learning outcomes (ability to...):
- (NCATE-9) Students will demonstrate computational proficiency, including a conceptual understanding of numbers, ways of representing number, relationships among number and number systems, and the meanings of operations.
- (NCATE-12) Students demonstrate an understanding of concepts and practices related to data analysis, statistics, and probability.
- Students will use manipulatives to model mathematical concepts.
- Students will use handheld and computer technology to explore probability concepts including simulations.

- Cluster: Math Education

- Catalog Entry
- Abbreviated Title: Elementary Topics in Math II
- Nickname: ElemTopII
- Credits: 3
- Grades: A-F
- Description: Elementary Topics in Mathematics I&II is a sequence for majors in elementary education and related fields. The course focuses on the development of geometry and algebra. Students use both dynamic geometry software and graphing calculators to develop representation, communication, and problem solving processes in both algebra and geometry. Does not apply to Arts and Sciences natural science requirements.
- Prerequisites: 1101 Elementary Topics in Math I
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 121, 122 Elem Topics in Math
- Sample textbook: O'Daffer, P., Charles, R., Cooney, T., Dossey, J., Schielack, J. (2008). Mathematics for Elementary School Teachers (4 ed.). NY: Addison-Wesley.
- Topics:
- 1 Angles and figure classifs, Ntwrks and prob. solv., intro. to dynamic geom. software
- 2 Triangle concurrency, constructions, the Euler Line, Tangrams
- 3 Circle and polygon angles, congruency, Geoboards
- 4 Pythagorean theorem, quadrilaterals
- 5 Transformations, symmetry; 6 Similarity, geometric patterns, dilations
- 7 tessellations, regular polyhedra, 3-D symmetry
- 8 coordinate geometry, measurement
- 9 perimeter and area, formulas for area
- 10 Surface area and volume, advanced functions of dynamic geometry software
- 11 Variables and expressions, solving equations
- 12 linear graphs, introduction to the graphing calculator
- 13 Quadratic and exponential graphs
- 14 Connecting algebra and geometry, distance and midpoint formulas
- 15 Modeling with algebra, solving word problems
- 16 Graphical representation and interpretation, supporting algebra with dynamic geometry software

- Desired learning outcomes (ability to...):
- (NCATE-10) Students emphasize relationships among quantities including functions, ways of representing mathematical relationships, and the analysis of change.
- (NCATE-11) Students use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties.
- (NCATE-13) Students apply and use measurement concepts and tools.
- Students will use dynamic geometry software to experiment, form and test conjectures, and to communicate geometric relationships.
- Students will use handheld and computer technology to explore various algebraic relationships and representations.

- Cluster: Math Education

- Catalog Entry
- Abbreviated Title: College Algebra
- Nickname: CollAlg
- Credits: 4
- Grades: A-F
- Description: A course on equations, functions and graphs, including linear equations and systems, polynomials and rational functions and equations, exponential and logarithmic functions, and inequalities. Students who will not need MATH 1200 for their intended majors or as a prerequisite for other classes should consider MATH 1090, MATH 1250, MATH 1260, or another Tier I quantitative skills course instead.
- Prerequisites: (PL1 or C or T or better in D004 Intermediate Algebra with PreAlgebra or C or T or better in D005 Intermediate Algebra)
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 113 College Algebra
- Sample textbook: College Algebra Essentials, Julie Miller, ISBN 1259168433, McGraw-Hill.
- Topics:
- Review of Prerequisites, Sets & the Real Number Line
- Models, Algebraic Expressions, Properties of Real Numbers
- Integer Exponents and Scientific Notation, Rational Exponents, Radicals
- Polynomials, Multiplication of Radicals, Simplifying Algebraic Expressions
- Factoring, Rational Expressions and More Operations on Radicals
- Equations and Inequalities, Linear & Rational Equations
- Applications & Modeling with Linear Equations
- Complex Numbers, Quadratic Equations and Applications
- Linear Inequalities & Compound Inequalities, Absolute Value Eqns. & Inequalities
- Functions and Graphs, Circles, Functions \& Relations
- Linear Equations in 2 Variables & Linear Functions, Applications of Linear Eqns. & Modeling
- Comparing Graphs of Equations, Transformations of Graphs
- Analyzing Graphs of Functions & Piecewise-Defined Functions
- Algebra of Functions & Function Composition, Variation
- Quadratic Functions & Applications, Polynomial Functions
- Division of Polynomials & the Remainder & Factor Theorems
- Zeros of Polynomials, Rational Functions, Polynomial & Rational Inequalities
- Inverse Functions, Exponential and Logarithmic Functions
- Exponential & Logarithmic Equations, Modeling with Exp. & Log. Functions
- Systems of Linear Equations in two Variables & Applications

- Desired learning outcomes (ability to...):
- 1. Functions:
- 1.1 Represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, exponential, logarithmic and piecewise-defined functions.
- 1.2 Determine whether an algebraic relation or given graph represents a function.
- 1.3 Perform transformations of functions: translations, reflections and stretching and shrinking.
- 1.4 Perform operations with functions: addition, subtraction, multiplication, division and composition.
- 1.5 Analyze the algebraic structure and graph of a function, including those listed in (1.1), to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function, asymptotes, whether the function is one-to-one, whether the graph has symmetry (even/odd), etc., and given the graph of a function to determine possible algebraic definitions.
- 1.6 Find inverses of functions listed in (1.1) and understand the relationship of the graph of a function to that of its inverse.
- 1.7 Use the Remainder and Factor Theorems for polynomial functions.
- 1.8 Use functions, including those listed in (1.1), to model a variety of real-world problem solving applications.
- 2. Equations/Systems:
- 2.1 Understand the difference between an algebraic equation of one, two or more variables and a function, and the relationship among the solutions of an equation in one variable, the zeros of the corresponding function, and the coordinates of the x-intercepts of the graph of that function.
- 2.2 Determine algebraically and graphically whether the graph of an equation exhibits symmetry.
- 2.3 Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, including equations arising in application problems.
- 2.4 Solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.
- 2.5 Solve polynomial and rational inequalities graphically and algebraically.

- Cluster: Lower Undergraduate
- Notes: This is an Ohio Transfer Assurance Guides (TAGS) course. The course is designed to closely follow the outcomes prescribed by TMM 001 College Algebra.

- Catalog Entry
- Abbreviated Title: Game Theory
- Nickname: GameTh
- Credits: 3
- Grades: A-F
- Description: Mathematical models for situations of conflict, whether actual or recreational. Matrix, 2- person, n-person, zero-sum and nonzero-sum games, Nash equilibria, cooperation and the prisoner's dilemma. Application to fields such as environmental policy, business decisions, football, warfare, evolution, and poker. Algebra, geometry and probability skills, includ- ing matrix manipulation, linear and quadratic equations, graphing equations, extracting information from graphs, determining probabilities and expectation values.
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 147 Intro Game Theory
- Sample textbook: Introducation to Game Theory, Straffin
- Topics:
- Nature of Games, Matrix Games: Dominance and Saddle Points
- Matrix Games: Mixed Strategies
- Applications: Anthropology: Jamaican Fishing; Warfare: Guerrillas, Police and Missiles
- Game Trees: Poker, Missiles
- Application to Business: Competitive Decision Making
- Games Against Nature
- Two-person Non-Zero-Sum Games, Nash Equilibria
- The Prisoner's Dilemma, Strategic Moves
- Application to Biology: Evolutionarily Stable Strategies
- The Nash Arbitration Scheme
- N-Person Games, Application to Politics: Strategic Voting
- N-Person Prisoner's Dilemma, Tragedy of the Commons
- Application to Athletics: Prisoner's Dilemma and the Football Draft
- Imputations, Combination and Stable Sets
- Application to Anthropology: Pathan Organization

- Desired learning outcomes (ability to...):
- Model two entity conflicts, both zero- and non-zero-sum, as matrix games.
- Find dominance, saddle-points and mixed strategies for zero-sum and interpret their meanings in applications.
- Model game by game trees and calculate expected payoffs for branches.
- Calculate Nash Equilibria in non-zero-sum games and identify stability and Pareto optimality of solutions.
- Verify/disprove the axioms of utility and fairness in matrix games.
- Calculate outcomes and find winning strategies in simple combinatorial games.
- Use linear equations, quadratic equations and their graphs in the above contexts.
- Use the basic axioms and methods of discrete probability in the above contexts.
- Recognize game theory as a mathematical tool that is applicable in a large variety of contexts.
- Understand that non-linear problems can have surprising consequences, such as random winning strategies, existence of multiple solutions and non-existence of acceptable solutions.

- Cluster: Lower Undergraduate
- Notes: Tier I. Can be used as a prerequisite for MATH 2500 Intro Statistics.

- Catalog Entry
- Abbreviated Title: Finite Math
- Nickname: Finite
- Credits: 3
- Grades: A-F
- Description: A course in the use of intermediate algebraic and combinatorial techniques in the context of common business applications. Topics include systems of linear equations and matrices, linear programming, mathematics of finance (compound interest, annuities, amortization), sets, counting and elementary probability.
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 150 Finite Math
- Sample textbook: Tan, Finite Mathematics for the Managerial, Life, and Social Sciences (7th ed), Thomson Brooks/Cole
- Topics:
- Systems of linear equations and matrices
- Geometric Linear Programming
- Mathematics of Finance (compound interest, annuities, amortization)
- Sets and counting
- Elementary probability

- Desired learning outcomes (ability to...):
- Students can use linear equations to model and solve application problems.
- Students can recognize optimization problems and use linear programming as a tool to find solutions.
- Students can use the techniques of intermediate algebra in a variety of contexts.
- Students can use elementary finite probabilities and expectation values in application problems.
- Students can use vector and matrix notations.

- Cluster: Lower Undergraduate

- Catalog Entry
- Abbreviated Title: Pre-Calculus
- Nickname: PreCalc
- Credits: 4
- Grades: A-F
- Description: Course provides a rigorous treatment of graphs, inverses, and algebraic operations of polynomial, rational, exponential, logarithmic, and trigonometric functions, trigonometry and analytic geometry and an introduction to linear systems, polar coordinates, vectors and conic sections. Recommended only for students intending to enroll in MATH 2301 Calculus I. Students should concurrently register for MATH D300 PLTL for PreCalculus to make the course automatically transferable within Ohio.
- Prerequisites: (PL2 or C or T or better in 1200 College Algebra or C or T or better in 1321 Elementary Applied Mathematics I)
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 115 Pre-Calculus
- Sample textbook: Precalculus, J. Douglas Faires and James DeFranza
- Topics:
- Functions, Linear functions, Quadratic Functions
- Other Common Functions, Arithmetic Combinations of Functions
- Composition of Functions, Inverse Functions
- Polynomials, Factors and Zeros of Polynomials
- Rational Functions, Other Algebraic Functions
- Measuring Angles, Sine and Cosine Functions
- Basic Trigonometric Graphs, Other Trigonometric Functions
- Trigonometric Identities, Right-Triangle Trigonometry
- Inverse Trig Functions, Applications of Trig
- Exponential Functions, Natural Exponential Function, Logarithms, Exponential Growth and Decay
- Parabolas, Ellipses and Hyperbolas
- Polynomial and Rational Inequalities
- Intro to Systems of Linear Equations
- Intro to Vectors, Operations and Applications of Vectors
- Intro to Sequences and Series, Sums of Arithmetic and Geometric Series

- Desired learning outcomes (ability to...):
- 1. Functions:
- 1.1 Represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, piecewise-defined, exponential, logarithmic, trigonometric and inverse trigonometric functions.
- 1.2 Determine whether an algebraic relation or given graph represents a function.
- 1.3 Perform transformations of functions: translations, reflections and stretching and shrinking.
- 1.4 Perform operations with functions: addition, subtraction, multiplication, division and composition.
- 1.5 Analyze the algebraic structure and graph of a function, including those listed in (1.1), to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function, asymptotes, whether the function is one-to-one, whether the graph has symmetry (even/odd), etc., and given the graph of a function to determine possible algebraic definitions.
- 1.6 Find inverses of functions listed in (1.1) and understand the relationship of the graph of a function to that of its inverse.
- 1.7 Use the Remainder and Factor Theorems for polynomial functions.
- 1.8 Use functions, including those listed in (1.1), to model a variety of real-world problem solving applications.
- 2. Equations/Systems:
- 2.1 Understand the difference between an algebraic equation of one, two or more variables and a function, and the relationship among the solutions of an equation in one variable, the zeros of the corresponding function, and the coordinates of the x-intercepts of the graph of that function.
- 2.2 Determine algebraically and graphically whether the graph of an equation exhibits symmetry.
- 2.3 Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, trigonometric and inverse trigonometric, including equations arising in application problems.
- 2.4 Solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.
- 2.5 Identify and express the conics (quadratic equations in two variables) in standard rectangular form, graph the conics, and solve applied problems involving conics.
- 2.6 Solve polynomial and rational inequalities graphically and algebraically.
- 3. Sequences/Series:
- 3.1 Represent sequences verbally, numerically, graphically and algebraically, including both the general term and recursively.
- 3.2 Write series in summation notation, and represent sequences of partial sums verbally, numerically and graphically.
- 3.3 Identify and express the general term of arithmetic and geometric sequences, and find the sum of arithmetic and geometric series
- 4. More Trigonometry:
- 4.1 Express angles in both degree and radian measure.
- 4.2 Define the six trigonometric functions in terms of right triangles and the unit circle.
- 4.3 Solve right and oblique triangles in degrees and radians for both special and non-special angles, and solve application problems that involve right and oblique triangles.
- 4.4 Verify trigonometric identities by algebraically manipulating trigonometric expressions using fundamental trigonometric identities, including the Pythagorean, sum and difference of angles, double-angle and half-angle identities.
- 4.5 Solve a variety of trigonometric and inverse trigonometric equations, including those requiring the use of the fundamental trigonometric identities listed in (4.4), in degrees and radians for both special and non-special angles. Solve application problems that involve such equations.
- 5. Vectors:
- 5.1 Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane.
- 5.2 Perform basic vector operations both graphically and algebraically: addition, subtraction and scalar multiplication.
- 5.3 Solve application problems using vectors.

- Cluster: Lower Undergraduate
- Notes: This is an Ohio Transfer Assurance Guides (TAGS) course. The course is designed to closely follow the outcomes prescribed by TMM 002 Pre-Calculus.

- Catalog Entry
- Abbreviated Title: Elem Applied Math I
- Nickname: ElemAppMthI
- Credits: 3
- Grades: A-F
- Description: Course provides a rigorous treatment of graphs, inverses, and algebraic operations of polynomial, rational, exponential and logarithmic functions, equations and inequalities and an introduction to linear systems, sequences and series. Intended, together with MATH 1322, to prepare students for MATH 2301 Calculus I. Students cannot earn credit for both MATH 1200 and MATH 1321.
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 117
- Sample textbook: Precalculus: Mathematics for Calculus, Stewart/Redlin/Watson, 6th Edition
- Topics:
- Intro to Systems of Linear Equations
- Functions, Domain and range of a function, Graphs of functions
- Linear and Quadratic Functions and their Graphs
- Quadratic equations and inequalities
- Algebra (Arithmetic combination) of Functions
- Composition and Decomposition of Functions
- Average Rate of Change of a Function
- Transformations of Functions and Their Graphs
- One-to-one functions and inverse of a Function
- Polynomial Functions, Zeros of Polynomials and Factoring
- Dividing Polynomials, Complex Numbers
- Rational functions, Polynomial and Rational Equations and Inequalities
- Exponential and Logarithm Functions, Exponential Growth and Decay
- Intro to Sequences and Summation Notation, Sums of Arithmetic and Geometric Sequences

- Desired learning outcomes (ability to...):
- 1. Functions:
- 1.1 Represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, piecewise-defined, exponential, logarithmic.
- 1.2 Determine whether an algebraic relation or given graph represents a function.
- 1.3 Perform transformations of functions: translations, reflections and stretching and shrinking.
- 1.4 Perform operations with functions: addition, subtraction, multiplication, division and composition.
- 1.5 Analyze the algebraic structure and graph of a function, including those listed in (1.1), to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function, asymptotes, whether the function is one-to-one, whether the graph has symmetry (even/odd), etc., and given the graph of a function to determine possible algebraic definitions.
- 1.6 Find inverses of functions listed in (1.1) and understand the relationship of the graph of a function to that of its inverse.
- 1.7 Use the Remainder and Factor Theorems for polynomial functions.
- 1.8 Use functions, including those listed in (1.1), to model a variety of real-world problem solving applications.
- 2. Equations/Systems:
- 2.1 Understand the difference between an algebraic equation of one, two or more variables and a function, and the relationship among the solutions of an equation in one variable, the zeros of the corresponding function, and the coordinates of the x-intercepts of the graph of that function.
- 2.2 Determine algebraically and graphically whether the graph of an equation exhibits symmetry.
- 2.3 Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, including equations arising in application problems.
- 2.4 Solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.
- 2.6 Solve polynomial and rational inequalities graphically and algebraically.
- 3. Sequences/Series:
- 3.1 Represent sequences verbally, numerically, graphically and algebraically, including both the general term and recursively.
- 3.2 Write series in summation notation, and represent sequences of partial sums verbally, numerically and graphically.
- 3.3 Identify and express the general term of arithmetic and geometric sequences, and find the sum of arithmetic and geometric series.
- 16. Understand the average rate of change of the graph of a function or equation on an interval.

- Notes: This is an Ohio Transfer Assurance Guides (TAGS) course. The course is designed to closely follow the first half of the outcomes prescribed by TMM 002 Pre-Calculus.

- Catalog Entry
- Abbreviated Title: Elem Applied Math II
- Nickname: ElemAppMthII
- Credits: 3
- Grades: A-F
- Description: A rigorous course in trigonometry and analytic geometry including right angle trigonometry, trigonometric functions and their graphs, inverse trigonometric functions, trigonometric identities and equations and introductions to vectors, polar coordinates and conic sections. Intended, together with MATH 1321, to prepare students for MATH 2301 Calculus I. Students cannot earn credit for both MATH 1300 and MATH 1322.
- Prerequisites: (PL2 or C or T or better in 1321 Elementary Applied Mathematics I)
- Taught in: Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 118
- Sample textbook: Precalculus: Mathematics for Calculus, Stewart/Redlin/Watson, 6th Edition
- Topics:
- Measuring angles, the Unit Circle
- Trigonometric Functions and their Graphs
- Right Angle Trigonometry
- Inverse Trigonometric Functions and their Graphs
- Trigonometric Identities, Laws of Sines and Cosines
- Addition and Subtraction Formulas, Double-angle and Half-angle Formulas
- Sum-Product Identities, Trigonometric Equations
- Intro to Polar Coordinates
- Intro to Vectors in 2D, Dot Product
- Conic Sections

- Desired learning outcomes (ability to...):
- 1. Functions:
- 1.1 Represent trigonometric and inverse trigonometric functions verbally, numerically, graphically and algebraically; define the six trigonometric functions in terms of right triangles and the unit circle.
- 1.2 Perform transformations of trigonometric and inverse trigonometric functions: translations, reflections and stretching and shrinking (amplitude, period and phase shift).
- 1.3 Analyze the algebraic structure and graph of trigonometric and inverse trigonometric functions to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, asymptotes, whether the function is one-to-one, whether the graph has symmetry (even/odd), etc., and given the graph of a function to determine possible algebraic definitions.
- 1.4 Use trigonometric and inverse trigonometric functions to model a variety of real-world problem-solving applications.
- 2. Equations:
- 2.1 Solve a variety of trigonometric and inverse trigonometric equations, including those requiring the use of the fundamental trigonometric identities listed in (4.4), in degrees and radians for both special and non-special angles. Solve application problems that involve such equations.
- 2.5 Identify and express the conics (quadratic equations in two variables) in standard rectangular form, graph the conics, and solve applied problems involving conics.
- 3. Angles/Triangles:
- 3.1 Express angles in both degree and radian measure.
- 3.2 Solve right and oblique triangles in degrees and radians for both special and non-special angles, and solve application problems that involve right and oblique triangles.
- 4. Identities:
- 4.1 Verify trigonometric identities by algebraically manipulating trigonometric expressions using fundamental trigonometric identities, including the Pythagorean, sum and difference of angles, double-angle and half-angle identities.
- 5. Vectors:
- 5.1 Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane.
- 5.2 Perform basic vector operations both graphically and algebraically: addition, subtraction and scalar multiplication.
- 5.3 Solve application problems using vectors.
- 7. Convert points and equations between rectangular and polar form

- Notes: This is an Ohio Transfer Assurance Guides (TAGS) course. The course is designed to closely follow the outcomes prescribed by TMM 003 Trigonometry and the second half of the outcomes in TMM 002 Pre-Calculus.

- Catalog Entry
- Abbreviated Title: Survey of Calculus
- Nickname: SurvCalc
- Credits: 4
- Grades: A-F
- Description: Presents a survey of basic concepts of calculus. For students who want an introduction to calculus, but do not need the depth of 2301 and 2302. Note: Students cannot earn credit for both 1350 and 2301.
- Prerequisites: (PL2 or C or T or better in 1200 College Algebra or C or T or better in 1321 Elementary Applied Mathematics I)
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter courses: 163A Intro to Calculus I; 163B Intro to Calculus II.
- Sample textbook: Calculus for Business, Economics, Life Sciences, and Social Sciences, Eleventh Edition. Authors: Barnett, Ziegler, and Byleen. Publisher: Pearson/Prentice Hall, 2007. ISBN: 0-13-232818-6
- Topics:
- Linear Equations and Inequalities*; Graphs and Lines*; Functions
- Elementary Functions: Graphs and Transformations; Quadratic Functions; Exponential Functions;
- Logarithmic Functions; Introduction to Limits; Continuity; Infinite Limits and Limits at Infinity
- The Derivative; Basic Differentiation Properties; Differentials
- Marginal Analysis in Business and Economics; The Constant e and Continuous Compound Interest
- Derivatives of Exponential and Logarithmic Functions; Derivatives of Products and Quotients
- The Chain Rule; Implicit Differentiation; Related Rates
- First Derivative and Graphs; Second Derivative and Graphs; Curve Sketching Techniques
- Absolute Maxima & Minima; Optimization
- Antiderivatives and Indefinite Integrals; Integration by Substitution
- Differential Equations; Growth and Decay; The Definite Integral
- The Fundamental Theorem of Calculus; Area between Curves
- Applications in Business and Economics; Integration by Parts

- Desired learning outcomes (ability to...):
- Understand the business terminology of demand, cost, price, revenue, and profit.
- Use linear, polynomial, rational, algebraic, exponentail and logarithmic functions in business applications.
- Determine the limits of functions graphically, numerically, and analytically.
- Recognize and determine infinite limits and limits at infinity.
- Determine the continuity of functions at a point or on intervals.
- Understand the interpretation of the derivative as the slope of a line tangent to a graph and as the rate of change of a dependent variable with respect to an independent variable and determine the derivative of a function using the limit definition.
- Use differentials in approximation problems.
- Determine derivatives using the power rule, sum & difference rules, product rule, quotient rule, and chain rule.
- Determine derivatives of Exponential and Logarithmic Functions
- Understand the business terminology of marginal quantities, including marginal cost, marginal revenue, and marginal profit.
- Determine higher order derivatives of a function.
- Understand velocity as the derivative of position and acceleration as the 2nd derivative of position
- Determine the absolute extrema of a continuous function on a closed interval.
- Use the first and second derivatives to analyze and sketch the graph of a function, including determining intervals on which the graph is increasing, decreasing, constant, concave up, concave down, and finding relative extrema and inflection points.
- Apply differential calculus to business applications.
- Demonstrate the ability to determine indefnite integrals, use the Fundamental Theorem of Calculus, integrate by substitution and by parts.
- Use defnite integrals in applications such as determining the area of an enclosed region and fnding the average value of a function.
- Use and solve differential equations to model growth and decay.
- Apply integral calculus to business applications.

- Cluster: Lower Undergraduate
- Notes: TAGS course.

- Catalog Entry
- Abbreviated Title: Intro Geometry
- Nickname: Geom4MS
- Credits: 3
- Grades: A-F
- Description: Intended for middle childhood education majors. Core concepts and principles of Euclidean geometry in two- and three-dimensions. Informal and formal proof. Measurement. Properties and relations of geometric shapes and structures. Symmetry. Transformational geometry. Tessellations. Congruence and similarity. Coordinate geometry. Constructions. Historical development of Euclidean and non-Euclidean geometries including contributions from diverse cultures. Dynamic Geometry Software to build and manipulate representations of two- and three- dimensional objects.
- Prerequisites: (1300 Pre-Calculus or 1322 Elementary Applied Mathematics II or PL3), Education Major
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter course: 330A
- Sample textbook: Aichele, D. & Wolfe, J. (2008). Geometric structures: An inquiry-based approach for prospective elementary and middle school teachers. NY: Pearson; Beem, J. (2006). Geometry connections. NY: Prentice Hall; Reynolds, B. & Fenton, W. (2006). College geometry using the Geometer's Sketchpad. Emeryville, CA: Key College Publishing.
- Topics:
- See description above

- Desired learning outcomes (ability to...):
- (NCATE-11) Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties, including:
- 11.1 Demonstrate knowledge of core concepts and principles of Euclidean geometry in two and three dimensions.
- 11.2 Exhibit knowledge of informal proof.
- 11.3 Build and manipulate representations of two- and three-dimensional objects and perceive an object from different perspectives.
- 11.4 Specify locations and describe spatial relationships using coordinate geometry.
- 11.5 Analyze properties and relationships of geometric shapes and structures.
- 11.6 Apply transformation and use congruence, similarity, and line or rotational symmetry.

- Cluster: Math Education

- Catalog Entry
- Abbreviated Title: Calculus I
- Nickname: CalcI
- Credits: 4
- Grades: A-F
- Description: First course in calculus and analytic geometry with applications in the sciences and engineering. Includes basic techniques of differentiation and integration with applications including rates of change, optimization problems, and curve sketching; includes exponential, logarithmic and trigonometric functions.
- Prerequisites: (PL3 or C or T or better in 1300 Pre-Calculus or C or T or better in 1322 Elementary Applied Mathematics II or B or better in 1350 Survey of Calculus)
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 263A,B Calculus
- Sample textbook: Essential Calculus with Early Transcendentals, by J. Stewart
- Topics:
- Week 1: The Limit of a Function, Calculating Limits, Continuity
- Week 2: Limits involving infinity, Derivatives and Rates of Change
- Week 3: Basic Differentiation Formulas - polynomials & trig functions, Product and Quotient Rules
- Week 4: The Chain Rule, Implicit Differentiation
- Week 5: Related Rates, Linear Approx. & Differentials
- Week 6: Inverse Functions and Logarithms, Derivatives of Log & Exp Funcs.
- Week 7: Inverse Trig. Functions, Maximum and Minimum Values
- Week 8: Max. & Min. Values, The Mean Value Theorem
- Week 9: Derivatives and the Shape of a Graph
- Week 10: More Curve Sketching
- Week 11: Applied Optimization Problems, Newton's Method
- Week 12: Antiderivatives, Areas and Distances
- Week 13: The Definite Integral, Evaluating Definite integrals
- Week 14: Fundamental Theorem of Calculus, The Substitution Rule

- Desired learning outcomes (ability to...):
- Students can use the tools of differential and integral calculus in a variety of applications

- Cluster: Lower Undergraduate
- Notes: This is a TAGS course and the above topics follow closely the outcomes prescriped by TAGS

- Catalog Entry
- Abbreviated Title: Calculus II
- Nickname: CalcII
- Credits: 4
- Grades: A-F
- Description: Second course in calculus and analytic geometry with applications in the sciences and engineering. Includes techniques of integration, conic sections, polar coordinates, infinite series, vectors and vector operations.
- Prerequisites: C or T or better in 2301 Calculus I
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 263B,C Calculus
- Sample textbook: Essential Calculus with Early Transcendentals, by J. Stewart
- Topics:
- Week 1: Integration by Parts, Partial Fractions
- Week 2: Approximate Integration, Indeterminate Forms & L'Hopital's Rule
- Week 3: Improper integrals, Areas between curves
- Week 4: Volumes, Applications in Physics & Engineering
- Week 5: Applications cont., Differential Equations
- Week 6: Sequences, The Integral and Comparison Tests
- Week 7: Other Convergence Tests, Power Series
- Week 8: Representations as Power Series
- Week 9: Taylor and Maclaurin Series
- Week 10: Applications of Taylor Polynomials
- Week 11: Curves Defined by Parametric Eqs., Calculus with Parametric Curves
- Week 12: Polar Coordinates, Conic Sections
- Week 13: 3-D Coordinate Systems, Vectors
- Week 14: Dot Product, Cross Product

- Desired learning outcomes (ability to...):
- Students can use the tools of differential and integral calculus in a variety of applications

- Cluster: Lower Undergraduate

- Catalog Entry
- Abbreviated Title: Introduction to Statistics
- Nickname: IntStats
- Credits: 4
- Grades: A-F
- Description: An introductory course in applied statistics. Organization of data, central tendency and dispersion, descriptive bivariate data, correlation,designed experiments, probability, random variables, binomial and normal distributions, distributions, inferences from large samples, estimation,confidence intervals and hypothesis testing. Students cannot earn credit for MATH 2500 and any of the following: COMS 3520, ECON 3810, GEOG 2710, ISE 3040, ISE 3200, PSY 1110, PSY 2110, QBA 2010.
- Prerequisites: (PL2 or C or T or better in 1200 College Algebra or C or T or better in 1250 Introduction to Game Theory or C or T or better in 1260 Finite Math or C or T or better in 1321 Elementary Applied Mathematics I)
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 250, 251
- Sample textbook: Statistics, Principles and Methods, 6E, 2010, by Johnson and Bhattacharyya.
- Topics:
- Introduction to Statistical Methods
- Organization & Description of Data, Measures of Center, Measures of Variation
- Descriptive Bivariate Data, Designed Experiments, Correlation Coefficient, Prediction
- Elementary Probability, Conditional Probablity, Random Sampling
- Random Variables, Bernoulli Trials
- Continuous R.V., Normal Distribution
- Sampling Dist. of a Statistic, Central Limit Theorem
- Inferences from Large Samples, Point Estimation
- Confidence Interval, Hypothesis Testing, Inferences about Proportion
- Optional additional topics in elementary statistics and probability

- Desired learning outcomes (ability to...):
- Select and produce appropriate graphical, tabular, and numerical summaries of the distributions of variables in a data set. Summarize such information into verbal descriptions
- Summarize relationships in bivariate data using graphical, tabular, and numerical methods including scatter plots, two-way tables, correlation coefficients, and least squares regression lines
- Investigate and describe the relationships or associations between two variables using caution in interpreting correlation and association
- Use the normal distribution to interpret z-scores and compute probabilities
- Understand the principles of observational and experimental studies including sampling methods, randomization, replication and control
- Understand how the type of data collection can affect the types of conclusions that can be drawn
- Construct a model for a random phenomenon using outcomes, events, and the assignment of probabilities. Use the addition rule for disjoint events and the multiplication rule for independent events
- Compute conditional probabilities in the context of two-way tables
- Introduce the concept of a sampling distribution. Discuss the distribution of the sample mean and sample proportion under repeated sampling (Central Limit Theorem)
- Understand the dependence of margin of error on sample size and confidence level
- Students should be expected to simulate or generate sampling distributions to observe, empirically, the Central Limit Theorem
- Estimate a population mean or proportion using a point estimate and confidence intervals , and interpret the confidence level and margin of error
- Determine the appropriate sample size for a specific margin of error and confidence level
- Given a research question involving a single population, formulate null and alternative hypotheses. Describe the logic and framework of the inference of hypothesis testing
- Make a decision using a p-value and draw an appropriate conclusion. Interpret statistical significance
- Carry out a hypothesis test for a mean or proportion. Interpret statistical and practical significance in this setting
- Perform interval estimation and hypotheses testing for two-sample problems (e.g., difference of two means or proportions and chi-square test of independence)

- Cluster: Lower Undergraduate, Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: History of Mathematics
- Nickname: HistMath
- Credits: 3
- Grades: A-F
- Description: Main lines of mathematical development in terms of contributions made by great mathematicians: Euclid, Archimedes, Descartes, Newton, Gauss, etc.
- Prerequisites: 2301 Calculus I
- Crosslisted with: 5000 History of Mathematics
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 300 History of Mathematics
- Sample textbook: Dunham, W. (1991). Journey through Genius: The Great Theorems of Mathematics. Penguin. or Berlinghoff, W. and Gouvea, F. (2003). Math through the Ages: A Gentle History for Teachers and Others. Oxton House Publishing, 2 edition. or Katz, V. J. (2009). A history of mathematics: An introduction (3rd ed.). Boston: Addison-Wesley.
- Topics:
- Proto-mathematics and the development of numeration
- Egyptian, Indian and Babylonian contributions
- Greek Mathematics
- Renaissance and Modern mathematical development.
- Topics span disciplines of algebra, geometry, number theory, calculus, discrete mathematics.

- Desired learning outcomes (ability to...):
- Students will be able to apply historical methods to mathematical histories and to critically analyze mathematical histories.
- Students will see the development of mathematics beyond western mathematics and will understand the nature of mathematics as process and discipline.
- Students will demonstrate working knowledge of key moments and figures in mathematics history.
- Students will understand the role of histories of mathematics in their chosen field.
- Students should develop an understanding of instructional strategies that enhance student learning.

- Cluster: Math Education

- Catalog Entry
- Abbreviated Title: Discrete Math
- Nickname: Discrete
- Credits: 3
- Grades: A-F
- Description: Introduction to discrete mathematical structures and their applications. The main topics are induction and recursion, graph theory and counting techniques. Applications include discrete and network optimization, discrete probability, game theory and voting systems.
- Prerequisites: 2301 Calculus I
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 308 Discrete Math
- Sample textbook: Discrete Mathematics with Applications, by S. Epp, 3rd edition
- Topics:
- Week 1: Induction
- Week 2: Recursion, Sequences defined by Recursive and Explicit Formulas
- Week 3: Set Theory, Set Operations, De Morgan's Laws, Power Set, Venn Diagrams
- Week 4: Counting Techniques: Possibility Trees, Multiplication Rule, Permutations
- Week 5: Addition and Difference Rules, Inclusion-Exclusion Principle
- Week 6: Combinations, Binomial Formula
- Week 7: Counting Techniques in Discrete Probability
- Week 8: Graph Theory: Eulerian and Hamiltonian Cycles, Node Degrees, Connectivity
- Week 9: Properties of Trees, Minimum Spanning Trees, Evolutionary Trees
- Week 10: Graph Coloring, Graph Modeling
- Week 11: Analysis of Algorithms, Search & Sort Algorithms, Efficiency
- Week 12: Discrete Optimization, Traveling Salesman Problem, Shortest Path Problem
- Week 13: Maximum Flow Problem and Applications, Assignment Problem, Baseball Elimination Problem
- Week 14: Linear and Integer Programming, Modeling Techniques using Binary Variables

- Desired learning outcomes (ability to...):
- the ability to count or enumerate objects, perform combinatorial analysis to solve counting problems
- the ability to understand the mathematics of graphs and trees, how to use graphs as models in a variety of areas
- the ability to apply induction for proving properties of discrete structures
- the ability to use discrete structures in application areas like computer science, optimization, probability

- Cluster: Math Education, Algebraic Undergraduate, Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Elementary Number Theory
- Nickname: NumTh
- Credits: 3
- Grades: A-F
- Description: Investigation of properties of the natural numbers. Topics include mathematical induction, factorization, Euclidean algorithm, Diophantine equations, congruences, divisibility, multiplicative functions, and applications to cryptography.
- Prerequisites: (3050 Discrete Math or CS 3000)
- Crosslisted with: 5070 Elementary Number Theory
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 307 Number Theory
- Sample textbook: Elementary Number Theory and Its Applications, K. Rosen
- Topics:
- Week 1: The integers, Summation and products, induction
- Week 2: Binomial coefficients, divisibility, representations of integers
- Week 3: Computer operations and complexity, prime numbers
- Week 4 GCD, The Euclidean Algorithm, Prime Factorization
- Week 5 Fermat numbers and factorization methods, Mid-term 1
- Week 6: Linear Diophantine equations Congruences
- Week 7: Chinese remainder theorem, Systems of linear congruences
- Week 8: Pollard rho method, divisibility tests, perpetual calendar, Round-robin
- Week 9: Hashing, Check digits, Wilson's theorem and Fermat's little theorem
- Week 10: Psuedoprimes, Euler's Theorem, Mid-term 2
- Week 11: Euler's phi function, sum & number of divisors
- Week 12: Perfect numbers, Mersenne primes
- Week 13: Character ciphers, block ciphers, exponentiation ciphers
- Week 14: Public-key cryptography
- Week 15: Knapsack ciphers, some applications to computer science

- Desired learning outcomes (ability to...):
- Students can construct proofs of fundatmental results in number theory
- Students understand how number theory is important in modern applications

- Cluster: Math Education, Algebraic Undergraduate

- Catalog Entry
- Abbreviated Title: College Geometry
- Nickname: CollGeom
- Credits: 3
- Grades: A-F
- Description: An axiomatic approach to Euclidean geometry. A core batch of theorems of Euclidean geometry are proven, and interesting geometric problems are solved using the axioms and theorems. Additional concepts and techniques -- such as similarity, transformations, coordinate systems, vectors, matrix representations of transformations, complex numbers, and symmetry -- are introduced as ways of simplifying the proofs of theorems or the solutions of geometric problems. Hyperbolic geometry is introduced from an axiomatic standpoint, primarily to illustrate the independence of the Parallel Postulate. Computers are used to produce dynamic drawings to illustrate theorems and problems.
- Prerequisites: (3050 Discrete Math or CS 3000), (3200 Applied Linear Algebra or 3210 Linear Algebra)
- Crosslisted with: 5110 College Geometry
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 330B
- Sample textbook: Greenberg: Euclidean and Non-Euclidean Geometries, Fourth Edition (Freeman, 2008), Hartshorne: Geometry : Euclid and Beyond (Springer, 2000), Moise: Elementary Geometry from an Advanced Standpoint, Third Edition (Addison Wesley, 1990), or Wallace and West: Roads to Geometry, Third Edition (Pearson, 2004)
- Topics:
- Introduction to Axiom Systems
- Introduction to Software for Producing Dynamic Geometric Drawings
- Axiomatic approach to Neutral Geometry
- Axiomatic approach to Euclidean Geometry
- Similarity
- Transformations
- Coordinates, Vectors, Matrix representations of transformations
- Complex Numbers and Geometry
- Symmetry
- Axiomatic approach to Hyperbolic Geometry

- Desired learning outcomes (ability to...):
- Prove a core batch of the standard theorems of Neutral, Euclidean, and Hyperbolic Geometry using deductive, axiom-based proofs.
- Demonstrate the independence of the Parallel Postulate using examples from Euclidean and Hyperbolic Geometry.
- Demonstrate the dependence of some of the axioms commonly included in axiom sets for high school math books.
- Solve geometric problems using the axioms and theorems of Euclidean Geometry.
- Incorporate methods of similarity, transformations, coordinates, vectors, matrices, complex numbers, and symmetry to simplify proofs or solve geometric problems.
- Use computer programs to produce dynamic drawings to illustrate geometric theorems and problems.

- Cluster: Math Education

- Catalog Entry
- Abbreviated Title: Applied Linear Algebra
- Nickname: AppLinAlg
- Credits: 3
- Grades: A-F
- Description: A course on linear algebra with an emphasis on applications and computations. Solutions to linear systems, matrices and matrix algebra, n-dimensional real vector spaces and subspaces, bases and dimension, eigenvalues and eigenvectors, diagonalization, norms, inner product spaces, orthogonality and least squares problems.
- Prerequisites: 2301 Calculus I
- Crosslisted with: 5200 Applied Linear Algebra
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 410 Matrix Theory
- Sample textbook: Matrix Analysis and Applied Linear Algebra, by Carl D. Meyer
- Topics:
- Solutions to linear systems
- matrices and matrix algebra
- n-dimensional real vector spaces and subspaces
- bases and dimension
- eigenvalues and eigenvectors
- diagonalization
- inner product spaces and norms
- orthogonality and least squares problems

- Desired learning outcomes (ability to...):
- Students can competently carry out computations involving solutions of linear systems of equations and eigenvalues
- Students understand and can use the geometry of linear systems and matrices
- Students can effectively manipulate matrix equations
- Students can prove basic results of linear algebra

- Cluster: Algebraic Undergraduate

- Catalog Entry
- Abbreviated Title: Linear Algebra
- Nickname: LinAlg
- Credits: 3
- Grades: A-F
- Description: A course in linear algebra for students majoring or minoring in the mathematical sciences. The course will introduce both the practical and theoretical aspects of linear algebra and students will be expected to complete both computational and proof-oriented exercises. Topic covered will include: Solutions to linear systems, matrices and matrix algebra, determinants, n-dimensional real vector spaces and subspaces, bases and dimension, linear mappings, matrices of linear mappings, eigenvalues and eigenvectors, diagonalization, inner product spaces and norms, orthogonality and applications.
- Prerequisites: 2302 Calculus II, (3050 Discrete Math or CS 3000)
- Crosslisted with: 5210 Linear Algebra
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 411
- Sample textbook: Matrix Analysis and Applied Linear Algebra, by Carl D. Meyer
- Topics:
- Solutions to linear systems
- matrices and matrix algebra
- n-dimensional real vector spaces and subspaces
- bases and dimension
- eigenvalues and eigenvectors
- diagonalization
- inner product spaces and norms
- orthogonality and least squares problems

- Desired learning outcomes (ability to...):
- Students can competently carry out computations involving solutions of linear systems of equations and eigenvalues
- Students understand and can use the geometry of linear systems and matrices
- Students can effectively manipulate matrix equations
- Students can prove basic and intermediate results of linear algebra

- Cluster: Math Education, Algebraic Undergraduate, Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Abstract Algebra
- Nickname: AbsAlg
- Credits: 3
- Grades: A-F
- Description: An elementary introduction to algebraic structures. Mappings, relations, definitions, and examples of groups, groups of rotations, cyclic groups, Lagrange's Theorem, fields, polynomials over fields.
- Prerequisites: 3070 Elementary Number Theory, (3200 Applied Linear Algebra or 3210 Linear Algebra)
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 314
- Sample textbook: Gilbert and Gilbert
- Topics:
- Sets, relations, functions, one-to-one and onto functions
- equivalence relations, partitions, binary operations and their properties.
- Groups, elementary properties, subgroups, homomorphisms, normal subgroups, quotient groups
- Lagrange's Theorem, groups of permutations, Cayley's theorem.
- Rings, Ideals, ring homomorphisms, subrings, elementary properties, types of rings, quotient rings.

- Desired learning outcomes (ability to...):
- Students will develop awareness and appreciation of the axiomatic method as well as familiarity with basic algebraic structures.
- Students can prove elementary results about algebraic structures.

- Cluster: Math Education, Algebraic Undergraduate
- Notes: This course, designed for AYA Math students might not be offered, but those students might take 4201 Modern Algebra instead.

- Catalog Entry
- Abbreviated Title: Calculus III
- Nickname: CalcIII
- Credits: 4
- Grades: A-F
- Description: Third course in calculus and analytic geometry with applications in the sciences and engineering. Includes partial differentiation, multiple integrals, line and surface integrals, and the integral theorems of vector calculus.
- Prerequisites: 2302 Calculus II
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 263D Calculus
- Sample textbook: Essential Calculus with Early Transcendentals, by J. Stewart
- Topics:
- Week 1: Equations of Lines and Planes, Cylinders and Quadric Surfaces
- Week 2: Vectors Functions and Space Curves, Arc Length & Curvature, Motion in Space
- Week 3: Functions of Several Variables, Limits and Continuity, Partial Derivatives
- Week 4: Tangent Planes and Approximation, The Chain rule
- Week 5: Directional Derivatives and the Gradient
- Week 6: Maximum and Minimum Values
- Week 7: Lagrange Multipliers, Double Integrals Over Rectangles
- Week 8: Double Integrals On General Regions, Double Integrals in Polar Coord.
- Week 9: Applications of Double Integrals, Triple Integrals
- Week 10: Triple Integrals in Cylindrical & Spherical Coords.
- Week 11: Vector Fields, Line Integrals
- Week 12: Green's Theorem, Curl and Divergence
- Week 13: Parametric Surfaces, Surface Integrals
- Week 14: Stokes and Divergence Theorems

- Desired learning outcomes (ability to...):
- Students can use the tools of differential and integral calculus in higher dimensions

- Cluster: Math Education, Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Vector Analysis
- Nickname: VectAnal
- Credits: 3
- Grades: A-F
- Description: Vector algebra and its applications. Vector calculus and space curves. Scalar and vector fields, gradient, divergence, curl, and Laplacian. Line and surface integrals. Divergence theorem, Stokes' theorem, and Green's theorem.
- Prerequisites: 3300 Calculus III
- Crosslisted with: 5320 Vector Analysis
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 440 Vector Analysis
- Sample textbook: An Introduction to Vector Analysis by Steven A. Chapin
- Topics:
- Vectors, Dot Product
- Cross Product, Equations of Lines and Planes
- Vector Functions, Space Curves
- Scalar Fields: Directional Derivative and Gradient
- Vector Fields: Divergence and Curl
- Applications
- Line Integrals and Conservative Vector Fields
- Multiple Integrals: Cylindrical and Spherical Coordinates
- Surfaces and Surface Integrals
- Green's Theorem, The Divergence Theorem, and Stokes' Theorem
- Applications: Maxwell's Equations
- Curvilinear Coordinates, More Applications

- Desired learning outcomes (ability to...):
- Students will understand and be able to compute differential and integral quantities involving vectors.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Elem Diff Eqns
- Nickname: DiffEqns
- Credits: 3
- Grades: A-F
- Description: Introduction to ordinary differential equations and their use as models for applications with an emphasis on exact solution methods for linear equations and systems including Laplace transform methods.
- Prerequisites: 2302 Calculus II
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 340 Differential Equations
- Sample textbook: Elementary Differential Equations (6th Edition) by C. Henry Edwards and David E. Penney
- Topics:
- Week 1: Definitions and terminology; Initial values problems; Differential equations as models
- Week 2: First order ODEs
- Week 3: First order ODEs (cont.)
- Week 4: Modeling with first order ODEs
- Week 5: Higher order linear ODEs
- Week 6: Higher order linear ODEs (cont.)
- Week 7: Modeling with higher order ODEs: spring/mass systems
- Week 8: Series solutions at regular points
- Week 9: Laplace transform methods
- Week 10: Laplace transform methods (cont.)
- Week 11: Systems of linear first order ordinary differential equations
- Week 12: Systems of linear first order ODEs (cont.)
- Week 13: Systems of linear first order ODEs
- Week 14: Phase plane, stability of equilibria

- Desired learning outcomes (ability to...):
- Students understand the meaning of differential equations as models and the meaning of a solution
- Students can find analytic solutions of a variety of linear differential equations

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Probability
- Nickname: Prob
- Credits: 3
- Grades: A-F
- Description: A mathematical introduction to univariate probability theory, with basic applications to statistics.
- Prerequisites: 2302 Calculus II, (3050 Discrete Math or CS 3000), (2500 Introduction to Statistics or COMS 3520 or GEOG 2710 or GEOL 3050 or ISE 3040 or ISE 3200 or PSY 2110 or QBA 2010), Not ISE 3210
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 350
- Sample textbook: Mathematical Statistics with Applications, by Wackerly, Mendenhall and Scheaffer, 2008 (7th edition). Chapters 1-4.
- Topics:
- Introduction/Motivation; review of basic combinatorial results.
- Counting rules; sample space and events.
- Probabilities of an event; basic rules of probability.
- Conditional probability; independent events.
- Law of total probability; Bayes' Theorem.
- Random variables; discrete and continuous distribution; density function.
- Expectation; variance; higher moments.
- Special discrete distributions (Bernoulli, binomial, Poisson, geometric, negative binomial).
- Special continuous distributions (uniform, exponential, normal, gamma).
- Chebyshev inequality; moment generating function.
- More on moment-generating function.
- Central Limit Theorem; introduction to sampling distribution.
- Estimation and confidence interval for one sample mean/proportion/variance.
- Hypotheses testing for one sample mean, proportion, variance.

- Desired learning outcomes (ability to...):
- Find probabilities using various methods.
- Conduct simple mathematical proofs in a rigorous manner.
- Derive important characteristics (mean, variance, MGF) for frequently used distributions.
- Find confidence intervals and conduct simple hypotheses tests for univariate case.

- Cluster: Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Applied Numerical Methods
- Nickname: ApplNumMeth
- Credits: 3
- Grades: A-F
- Description: A survey of numerical methods for science, engineering, and mathematics students. Topics include: solutions of systems of linear and nonlinear equations, eigenvalues, numerical differentiation and integration, and numerical solution of ordinary and partial differential equations. The topics will be posed in a setting of problems intended for engineering students using MATLAB. The course will simultaneously introduce numerical methods, programming techniques, problem solving skills and the Matlab language, in a lecture-lab format.
- Prerequisites: 3400 Elementary Differential Equations
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 344 Numerical Methods for CE & ME
- Sample textbook: Introduction to Numerical Method and Matlab Programming for Engineers, Young and Mohlenkamp
- Topics:
- Newton's Method, Bisection and Secant Method
- Linear Systems: Accuracy, Condition Numbers and Pivoting
- LU Factorization
- Nonlinear Systems - Newton's Method
- Eigenvectors, Vibrational Modes
- Numerical Methods for Finding Eigenvalues
- Iterative Solution of Linear Systems
- Plotting Functions of Two Variables
- Double Integrals for Rectangles and Non-rectangles
- Numerical Differentiation
- The Main Sources of Error
- Reduction of Higher Order Equations to Systems
- Euler Methods, Higher Order Methods, Multi-step Methods
- ODE Boundary Value Problems and Finite Differences, Finite Difference Method - Nonlinear ODE
- Heat-Diffusion Equation-Explicit & Implicit Methods, Finite Difference Method for Steady State PDEs

- Desired learning outcomes (ability to...):
- The ability to use MATLAB as a programming tool to solve common engineering and scientific problems.
- Understand and know how to apply common numerical methods for solving equations and linear systems, integration and differential equations.
- The ability to define and understand the practical consequences of issues such as convergence, stability, computational cost, and error propagation as they apply to various numerical problems.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Quant Found Bioinfo
- Nickname: Bioinfo
- Credits: 3
- Grades: A-F
- Description: Bioinformatics is the science of extracting biologically relevant information from large sets of biomolecular data. The course will introduce students to the mathematical models, statistical techniques, and algorithms on which this process is based.
- Prerequisites: (2500 Introduction to Statistics or BIOS 1700 or EE 3713 or PBIO 3150 or (PBIO 1140 and PSY 2110))
- Crosslisted with: 5680 Quantitative Foundations for Bioinformatics
- Taught in: Fall
- Frequency: Every Second Year
- Replaces the quarter course: 387
- Sample textbook: An Introduction to Bioinformatics Algorithms, Neil C. Jones and Pavel A. Pevzner, MIT Press 2004. + Bioinformatics and Molecular Evolution, Paul C. Higgs and Teresa K. Atwood, Blackwell 2005.
- Topics:
- Mathematical models and algorithms
- Basic probability theory, Markov Chains
- Models of sequence evolution
- Pairwise sequence alignment
- Scoring an alignment: PAM and BLOSUM matrices
- Aligning a sequence against a data base: BLAST
- Multiple sequence alignment
- Gene finding; Hidden Markov Models
- Clustering with applications to phylogeny reconstruction and gene expression profiles

- Desired learning outcomes (ability to...):
- Ability to translate certain types of biological into mathematical ones.
- Ability to recognize which types of bioinformatics software will give solutions to the mathematical problems that correspond to given biological ones.
- Familiarity with the most basic algorithms that are used by these software tools.
- Ability to interpret the meaning of the output of these software tools in biological terms.
- Ability to understand how parameter choices will affect the output.
- Ability to recognize typical sources of uncertainty or outright invalid answers that occur in using these software tools.

- Cluster: Algebraic Undergraduate

- Catalog Entry
- Abbreviated Title: Teaching Math Sec Schools
- Nickname: TeachMath
- Credits: 3
- Grades: A-F
- Description: Selected topics related to teaching of mathematics in grades 7-12
- Prerequisites: 3110 College Geometry, Jr. or Sr. status, corequisite 4100L Teaching Mathematics in Secondary Schools Early Field Experience
- Crosslisted with: 5100 Teaching Mathematics in Secondary Schools
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter course: MATH 320L - Teaching of Mathematics in Secondary Schools
- Sample textbook: Brahier, D. (2009). Teaching secondary and middle school mathematics, 3e. ISBN:0205569196 Allyn & Bacon. and Ohio Department of Education. Ohio Academic Content Standards Grades K to 12 - Mathematics.
- Topics:
- Teaching mathematics in grades 7-12, including algebra, geometry, statistics, calculus.
- Meaningful use of technology.
- Differentiating instruction.
- Lesson planning.
- Professional resources.
- Early field experience.

- Desired learning outcomes (ability to...):
- Throughout the course, lectures, readings, written assignments, collaborative engagements, and popular cultural resources will help students achieve these outcomes. In particular, students will...
- 1. describe the significance, content, philosophy, and impact on reform of national and state standards (including achievement testing, the High School Graduation Test, and implications of CORE);
- 2. describe credible theories of learning mathematics including constructivism and its variants;
- 3. explain how research in mathematics education is conducted, reported, and applied to teaching and learning practices.
- 4. illustrate how to use technology (including graphing calculators, software, video, and the Internet while also identifying benefits and obstacles of technology to maximizing student learning (PPP1);
- 5. give examples of questioning strategies for the classroom that promote mathematical thinking and dialogue (discourse);
- 6. use multiple strategies to support mathematics instruction including differentiation to meet the needs of all learners;
- 7. recognize the essential parts of a lesson plan; prepare a lesson plan that includes outcomes, materials, structured sequence of experiences for students, a logical closure, a planned extension, and a plan for assessment;
- 8. describe a variety of strategies that teachers can use to promote positive classroom management and the role that effective lesson planning has on classroom environment;
- 9. use a variety of assessment strategies to collect data, including electronic means, regarding student academic progress and dispositional development, and to communicate assessment items to student as productive feedback;
- 10. participate in programs for professional growth in mathematics education, including NCTM, OCTM, OUCTM, journals, ORC, and understand the need for continuous professional improvement.
- 11. describe (and demonstrate in lesson planning) how to make the five mathematical processes - problem solving, reasoning and proof, communication, connections, and representation - the focus of an AYA mathematics program;
- 12. Criteria for assessing the appropriateness of various technologies will be a focus of this objective (PPP2);
- 13. identify, select, and use hardware and software technology resources to meet specific teaching and learning objectives (PPP4);
- 14. write instructional objectives at the knowledge/skill, conceptual, and application levels;
- 15. recognize the use of technology-enriched learning activities in the classroom and write lesson plans that make use of technology to address diverse student needs, as appropriate and available (PPP7, 17, 22);
- 16. recognize that each student has individual needs and illustrate how a variety of teaching approaches, including the use of manipulatives and the use of technology, can be used to appeal to the learning style of each student (PPP1, 3, 6);
- 17. exhibit facility with resources to gather field-tested ideas for use in one's own clasroom, including electronic resources (PPP10);
- 18. grow in his/her appreciation of the role of mathematics in the AYA curriculum;
- 19. continue to develop a positive disposition toward the field of mathematics;
- 20. understand the role of community, place, and parents in mathematics education;

- Cluster: Math Education

- Catalog Entry
- Abbreviated Title: Tch Math Field Exp
- Nickname: TchFld
- Credits: 1
- Grades: A-F
- Description: Early Field Experience for students in Teaching Mathematics in Secondary Schools.
- Grading Rubric: Same as Teaching Mathematics in Secondary Schools
- Prerequisites: corequisite 4100 Teaching Mathematics in Secondary Schools
- Crosslisted with: 5100L Teaching Mathematics in Secondary Schools Early Field Experience
- Taught in: Fall
- Frequency: Yearly
- Sample textbook: Same as Teaching Mathematics in Secondary Schools
- Topics:
- Same as Teaching Mathematics in Secondary Schools

- Desired learning outcomes (ability to...):
- Same as Teaching Mathematics in Secondary Schools

- Cluster: Math Education
- Notes: 4100+4100L replaces MATH 320L

- Catalog Entry
- Abbreviated Title: ADV PRSP MATH HS TCHRS
- Nickname: AdvPerTeach
- Credits: 3
- Grades: A-F
- Description: Key math content topics such as algebra, calculus, discrete mathematics, and mathematical modeling, studied throughout the AYA Math Content courses are revisited in light of their applicability to High School mathematics. Students will synthesize previous content knowledge and bring a depth of understanding of mathematics to topics and themes they will likely teach in a grades 8-12 setting. This course is intended as a final mathematics content course for AYA Mathematics majors.
- Grading Rubric: Outcomes will be assessed and grades determined primarily by written examinations and homework assignments. A project or presentation may also be used.
- Prerequisites: 3110 College Geometry, 3300 Calculus III, concurrent 3240 Abstract Algebra
- Taught in: Fall
- Frequency: Yearly
- Sample textbook: Usiskin, Z., Peressini, A., Marchisotto, E., & Stanley, D. (2003). Mathematics for high school teachers: An advanced perspective. Upper Saddle River, NJ: Pearson Education, Inc.
- Topics:
- Real Numbers, Complex Numbers, and Functions
- Equations, Integers and Polynomials
- Number System Structures
- Congruence, Distance, Similarity
- Trigonometry, Area and Volume
- Axiomatics, Euclidean Geometry
- Calculus
- Statistics, Data Analysis, and Probability
- Linear Algebra and Linear Programming

- Desired learning outcomes (ability to...):
- After completion of the course, the student will be able to contextualize the mathematics content learned for their program in the content they will teach at the high school level.
- In particular, the student will be able to perform, analyze, and see the connections between the following skills and concepts and to the application of these skills to high school mathematics instruction. The skills/processes include:
- Analyze the origins, representations, and applications of mathematical concepts.
- Analyze solutions of mathematical problems to determine: Alternative means of solving and / or representing the solution and Ways of extending and / or generalizing the problem.
- Explain the construction of the real and complex number systems and various ways of representing real and complex numbers.
- Describe the various ways of representing and defining of functions.
- Analyze common mathematical problems and real-world models using functions.
- Use the theory of functions in solving equations and inequalities.
- Construct and analyze proofs using mathematical inductions.
- Recognize and prove various logical equivalences to mathematical induction.
- Apply and prove the Division Algorithm and Euclidean Algorithm.
- Extend the Division and Euclidean Algorithm to polynomials.
- Develop and apply algebraic properties of modular arithmetic systems.
- Relate integer congruence to real-world applications.
- Prove and apply the Chinese Remainder Theorem.
- Relate properties of the real and complex number systems to general ordered fields.

- Cluster: Math Education
- Notes: outcomes based on Math 6743, U. West Georgia, Yazdani

- Catalog Entry
- Abbreviated Title: Modern Algebra I
- Nickname: ModAlgI
- Credits: 3
- Grades: A-F
- Description: Groups, permutation groups, subgroups, normal subgroups, quotient groups. Conjugate classes and class equation formula and its application to p-groups. Fundamental theorem on homomorphisms.
- Prerequisites: (3200 Applied Linear Algebra or 3210 Linear Algebra), (3050 Discrete Math or CS 3000)
- Crosslisted with: 5221 Modern Algebra I
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter courses: parts of 411 Linear Algebra; 413A Introduction to Modern Algebra.
- Sample textbook: Gallian, Contemporary Abstract Algebra.
- Topics:
- Groups, Cyclic Groups, Permutations Groups, Isomorphisms, Cosets
- Lagrange's Theorem, External and Internal Direct Products, Normal Subgroups and Factor Groups
- Group Homomorphisms, Cauchy's Theorem.
- The simplicity of the alternating group, Fundamental Theorem of Finite Abelian Groups.
- Introduction to Rings, Integral Domains, Ideals and Factor Rings, Ring Homomorphisms.

- Desired learning outcomes (ability to...):
- Students will enhance their understanding and appreciation of the axiomatic method as well as their familiarity with basic algebraic structures and their ability to write proofs.

- Cluster: Algebraic Undergraduate

- Catalog Entry
- Abbreviated Title: Modern Algebra II
- Nickname: ModAlgII
- Credits: 3
- Grades: A-F
- Description: Fundamental theorem on finite abelian groups and its consequences. Cauchy theorem and first Sylow theorem. Polynomial rings. UFD and Euclidean domains. Maximal ideals. Algebraic extensions and splitting fields. Fundamental theorem of Galois theory.
- Prerequisites: 4221 Modern Algebra I
- Crosslisted with: 5222 Modern Algebra II
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 413A,B Introduction to Modern Algebra
- Sample textbook: Gallian, Contemporary Abstract Algebra.
- Topics:
- Rings of Polynomials, Principal Ideal Domains, Unique Factorization Domains, Euclidean Domains
- The field of quotients of a domain. Field Extensions, Introduction to Galois Theory.

- Desired learning outcomes (ability to...):
- Students will enhance their understanding and appreciation of the axiomatic method as well as their familiarity with basic algebraic structures and their ability to write proofs.

- Cluster: Algebraic Undergraduate

- Catalog Entry
- Abbreviated Title: Algebraic Coding Theory
- Nickname: AlgCoding
- Credits: 3
- Grades: A-F
- Description: Encoding and decoding. Vector spaces over finite fields. Linear Codes, parity-check matrices, syndrome decoding, Hamming Codes, and Cyclic Codes.
- Prerequisites: (3200 Applied Linear Algebra or 3210 Linear Algebra)
- Crosslisted with: 5230 Introduction to Algebraic Coding Theory
- Taught in: Spring
- Frequency: Every Second Year
- Replaces the quarter course: 412 Introduction to Algebraic Coding Theory
- Sample textbook: Hankerson et al, Coding Theory and Cryptography the essentials.
- Topics:
- Encoding and decoding.
- Vector spaces over finite fields.
- Linear Codes, parity-check matrices, syndrome decoding, Hamming Codes, BCH and Cyclic Codes.
- Decoding BCH codes.

- Desired learning outcomes (ability to...):
- Students will learn about this important application of Modern Algebra.
- They will understand the criteria for goodness of the various error-correcting codes studied and will be able to do the appropriate calculations to design the codes and to use them to correct a prescribed number of errors.

- Cluster: Algebraic Undergraduate

- Catalog Entry
- Abbreviated Title: Advanced Calculus I
- Nickname: AdvCalcI
- Credits: 3
- Grades: A-F
- Description: A proof-based course on functions of one variable. Topics include properties of the real and complex numbers, metric spaces and basic topology, sequences and series, a careful study of limits and continuity, differentiation and Reimann-Stieltjes integration.
- Prerequisites: (3200 Applied Linear Algebra or 3210 Linear Algebra), 3300 Calculus III
- Crosslisted with: 5301 Advanced Calculus I
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter course: 460AB Advanced Calculus
- Sample textbook: Principles of Mathematical Analysis, Rudin
- Topics:
- properties of the real and complex numbers
- metric spaces and basic topology
- sequences and series
- limits and continuity
- differentiation
- Reimann-Stieltjes integration

- Desired learning outcomes (ability to...):
- Students can understand and can prove the foundations of calculus.
- Students are prepared for graduate study and research in mathematics.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Advanced Calculus II
- Nickname: AdvCalcII
- Credits: 3
- Grades: A-F
- Description: Sequences and series of functions, uniform convergence, power series and elementary functions, multidimensional differentiation and integration, special functions (as time permits)
- Prerequisites: 4301 Advanced Calculus I
- Crosslisted with: 5302 Advanced Calculus II
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 460BC Advanced Calculus
- Sample textbook: Principles of Mathematical Analysis, Rudin
- Topics:
- Sequences and series of functions
- uniform convergence
- power series and elementary functions
- multidimensional differentiation and integration
- special functions (optional)

- Desired learning outcomes (ability to...):
- Students can prove and use fundamental theorems about the convergence of functions.
- Students are prepared for graduate study and research in mathematics.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Complex Variables
- Nickname: Complex
- Credits: 3
- Grades: A-F
- Description: A first course in complex variables focused on developing analytic techniques that are useful in applications. The course is also essential for further study in mathematics and students will be expected to do some proofs. Topics will include: Analytic and harmonic functions, Cauchy integration and residue theorems, contour integration, Taylor and Laurent expansions, conformality and linear fractional transformations with applications.
- Prerequisites: 3300 Calculus III
- Crosslisted with: 5310 Complex Variables
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 470 Complex Variables
- Sample textbook: Complex Variables and Applications, Brown and Churchhill
- Topics:
- Analytic and harmonic functions
- Cauchy integration and residue theorems
- Contour integration and the Cauchy Integral formula
- Taylor and Laurent expansions
- Conformal mappings & their applications

- Desired learning outcomes (ability to...):
- Students can use complex variables as tool for applications.
- Students can prove basic theorems about analytic functions.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Hilbert Spaces
- Nickname: Hilbert
- Credits: 3
- Grades: A-F
- Description: A course in applied linear analysis, especially Hilbert spaces, for advanced undegraduate and graduate students in mathematics, the sciences or engineering. The course will introduce both the practical and theoretical aspects of linear analysis and students will be expected to complete both computational and proof-oriented exercises. Topic covered will include: Normed Vector Spaces, the spaces L1 and L2, Hilbert Spaces, orthonormal systems, linear operators on Hilbert space and applications to differential equations.
- Grading Rubric: Outcomes will be assessed and grades determined primarily by written examinations and homework assignments. A project or presentation may also be used.
- Prerequisites: 3400 Elementary Differential Equations, (3200 Applied Linear Algebra or 3210 Linear Algebra)
- Crosslisted with: 5330 Hilbert Spaces and Applications
- Taught in: Spring
- Frequency: Every Second Year
- Sample textbook: Introduction to Hilbert Spaces with Applications, Third Edition by Lokenath Debnath and Piotr Mikusinski
- Topics:
- Vector spaces, Linear independence, Basis and Dimension, Normed spaces
- Banach spaces, linear operators, contraction mappings
- L2(R), L1(R), C[a,b]
- Inner products, Hilbert spaces, orthogonal and orthonormal systems
- Strong and weak convergence
- Trigonometric Fourier Series, Orthogonal complements and projections
- Linear functionals and the Riesz representation theorem, Separable spaces
- Example of operators, the adjoint of an operator and self-adjoint operators
- Invertible, normal, isometric and unitary operators, positive and projection operators
- Compact operators, Eigenvalues and eigenvectors, Spectral Decomposition
- Fourier transform, Unbounded operators
- Applications to Differential and integral equation

- Desired learning outcomes (ability to...):
- Students: Will understand the concepts and properties of function spaces and their properties.
- Can prove basic properties of Hilbert spaces and other functions spaces.
- Can use Hilbert space techniques in applications.

- Cluster: Analytic Undergraduate
- Notes: Justification of new course: (1) Additional preparation for real analysis. This course will provide many examples of function spaces, opportunities to develop proof writing and motivating material for the 630X Real Analysis courses. (2) Background in functional analysis before the 640X PDE sequence. Currently these concepts have to be introduced in the DE courses. (3) This will be a good math elective for Physics students.--- We need to be a little careful about overlap with 4410 Fourier Series & PDE

- Catalog Entry
- Abbreviated Title: Differential Equations
- Nickname: AdvDiffEqns
- Credits: 3
- Grades: A-F
- Description: An introduction to the qualitative theory of differential equations, with emphasis on linear systems.
- Prerequisites: 3400 Elementary Differential Equations, (3200 Applied Linear Algebra or 3210 Linear Algebra)
- Crosslisted with: 5400 Advanced Differential Equations
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter course: 449 Advanced Differential Equations
- Sample textbook: F. Brauer and J. Nohel, The qualitative theory of ordinary differential equations or P. Waltman, A second course in ordinary differential equations.
- Topics:
- Linear Systems (homogeneous, nonhomogeneous, systems with constant coefficients, exponential matrix)
- Periodic coefficients (Floquet's theorem)
- Autonomous systems (two dimensional case; phase plane, critical points)
- Elementary existence theory (successive approximations)
- Elementary stability theory for linear systems.

- Desired learning outcomes (ability to...):
- Students will have a good understanding of linear systems of ordinary differential equations.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Fourier Methods
- Nickname: Four&PDE
- Credits: 3
- Grades: A-F
- Description: Representation of functions as sums of infinite series of trigonometric functions, Bessel functions, Legendre polynomials, or other sets of orthogonal functions. Use of such representations for solution of partial differential equations dealing with vibrations, heat flow, and other physical problems.
- Prerequisites: 3300 Calculus III, 3400 Elementary Differential Equations
- Crosslisted with: 5410 Fourier Analysis and Partial Differential Equations
- Taught in: Spring
- Frequency: 3 out of 4 Years
- Replaces the quarter course: 441 Fourier Analysis and Partial Differential Equations
- Sample textbook: David Powers, Boundary value problems and partial differential equations, Elsevier/Academic Press, 2006
- Topics:
- Fourier series and integrals
- The heat equation
- The wave equation
- The potential equation
- Equations in higher dimensions

- Desired learning outcomes (ability to...):
- Ability to use the separation of variables method in the study of classical equations of mathematical physics.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Applied Dynamical Systems
- Nickname: ApplDynSys
- Credits: 3
- Grades: A-F
- Description: A survey of applied dynamical systems for Scientists, Engineers and Mathematicians with an emphasis on continuous time models.
- Grading Rubric: Outcomes will be assessed and grades determined primarily by written examinations and homework assignments. A project or presentation may also be used.
- Prerequisites: 3400 Elementary Differential Equations, (3200 Applied Linear Algebra or 3210 Linear Algebra)
- Crosslisted with: 5470 Applied Dynamical Systems
- Taught in: Spring
- Frequency: Every Second Year
- Sample textbook: Differential Dynamical Systems by James Meiss
- Topics:
- Modeling and Examples
- Dynamical Systems Concepts
- Invariant Manifolds
- Phase Plane
- Chaotic Dynamics
- Bifurcation Theory
- Hamiltonian Dynamics

- Desired learning outcomes (ability to...):
- Students will understand the role of dynamical systems as models for applications.
- Students will understand the basic concepts of dynamical systems and how they are used.
- Students will have tools for the analysis of dynamical systems that arrise in applications

- Cluster: Analytic Undergraduate
- Notes: Justification of New Course: This course will serve the following purposes (1) Preparation for Research in Dynamical Systems. Young's grant provides for multiple graduate students over a 4 year period. Just and Uspenskiy are also active in D.S., and, Aizicovici and Vu also publish in D.S. journals. This research requires a background in the concepts of dynamical systems. (2) Breadth for Other Math Undergraduate and Graduate Students. Dynamical Systems is a large and important area of mathematics (MCS #37) . It touches parts of many other areas and we have expertise in this area. (3) Training in D.S. Methods for Non-Math Students. Peter Jung has often requested that Dr. Young teach this course for the benefit of his graduate students.

- Catalog Entry
- Abbreviated Title: Theory of Statistics
- Nickname: ThStats
- Credits: 3
- Grades: A-F
- Description: Probability distributions of one and several variables, sampling theory, estimation of parameters, confidence intervals, analysis of variance, correlation, and testing of statistical hypotheses.
- Prerequisites: 3300 Calculus III, 3500 Probability, (3200 Applied Linear Algebra or 3210 Linear Algebra)
- Crosslisted with: 5500 Theory of Statistics
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter course: 450A,B Theory of Statistics
- Sample textbook: Mathematical Statistics with Applications, by Wackerly, Mendenhall and Scheaffer, 2008 (7th edition). or John E. Freund's Mathematical Statistics with Applications, by Miller and Miller, 2004 (7th edition).
- Topics:
- Review of one-variable distribution and moments; multivariate distribution.
- Marginal distribution; conditional distribution; moment-generating function.
- Product moments; moments of linear combinations of random variables.
- Conditional expectation; multinomial distribution; bivariate normal distribution.
- Functions of random variables.
- Sampling distributions.
- Point estimation; unbiasedness; efficiency; consistency.
- Sufficiency; method of moments; Maximum likelihood estimator.
- Bayesian estimation.
- Confidence interval for one-sample mean, proportion, variance.
- Confidence interval for two-sample cases.
- Theory of hypotheses testing.
- Tests of hypotheses involving (two-sample) means, variances and proportions.
- Contingency table test; GOF-test.

- Desired learning outcomes (ability to...):
- Compute various probabilities and expectations by various methods.
- Find distributions of functions of random variables.
- Find a point estimator of a parameter using various methods.
- Analyze and compare different point estimators.
- Find a confidence interval for a parameter for various distributions.
- Conduct various standard hypotheses tests; compute the power functions; find the UMP test using Neyman-Pearson Lemma; find the likelihood-ratio test.

- Cluster: Statistics + Actuarial
- Notes: This may have other options for Non-Math prerequisistes.

- Catalog Entry
- Abbreviated Title: Applied Statistics
- Nickname: AppStats
- Credits: 3
- Grades: A-F
- Description: Applications of the theory of statistics, including hypotheses testing, regression and correlation analysis, experimental design, and nonparametric statistics.
- Prerequisites: 4500 Theory of Statistics
- Crosslisted with: 5510 Applied Statistics
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 450B,C Theory of Statistics
- Sample textbook: Mathematical Statistics with Applications, by Wackerly, Mendenhall and Scheaffer, 2008 (7th edition). or John E. Freund's Mathematical Statistics with Applications, by Miller and Miller, 2004 (7th edition).
- Topics:
- Simple linear regression model; method of least squares; normal regression analysis;
- normal correlation analysis; introduction to multiple linear regression.
- Experimental design; ANOVA models; one-way design;
- randomized-block design; factorial design; multiple comparisons.
- Nonparametric tests; the sign test; the signed-rank test;
- rank-sum tests; runs test; Spearman's rank correlation coefficient.

- Desired learning outcomes (ability to...):
- Analyze simple linear regression models; derive point estimators, confidence intervals, and test statistics.
- Apply the ANOVA model to the experimental design data.
- Use nonparametric method for hypotheses tests when the underlying conditions for parametric tests are violated.

- Cluster: Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Stochastic Processes
- Nickname: StochProc
- Credits: 3
- Grades: A-F
- Description: Markov chains, Poisson process, birth and death process, queuing, and related topics.
- Prerequisites: 4500 Theory of Statistics
- Crosslisted with: 5520 Stochastic Processes
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 451 Stochastic Processes
- Sample textbook: Introduction to Probability Models, by Sheldon M. Ross, 9th Edition, 2007.
- Topics:
- Conditioning techniques for finding probabilities and expectations.
- Markov chains; time reversible MC; MCMC methods.
- Exponential distribution and Poisson process; generalizations of the Poisson process.
- Continuous-time Markov chains; birth and death processes.
- Renewal theory and its applications.
- Queuing theory.

- Desired learning outcomes (ability to...):
- Use conditioning techniques to find probabilities and expectations.
- Understand and analyze important MC models.
- Analyze Poisson process and its generalizations.
- Analyze simple renewal processes and queuing models.

- Cluster: Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Statistical Computing
- Nickname: StatComp
- Credits: 3
- Grades: A-F
- Description: Introduction to computational statistics; Monte Carlo methods, bootstrap, data partitioning methods, EM algorithm, probability density estimation, Markov Chain Monte Carlo methods.
- Prerequisites: 4500 Theory of Statistics
- Crosslisted with: 5530 Statistical Computing
- Taught in: Spring
- Frequency: Yearly
- Replaces the quarter course: 452 Statistical Computing
- Sample textbook: Computational Statistics Handbook with MATLAB 2nd ed, 2007, by W. L. Martinez and A.R. Martinez. or Modern Applied Statistics with S, by W.N.Venables and B.D.Ripley, 2002 (4th edition).
- Topics:
- Introduction to the software package, e.g. SAS, S-plus, R, MATLAB, SPSS.
- Methods for generating random variables from specified probability distribution.
- Monte-Carlo method; bootstrap; jackknife; cross-validation.
- EM algorithm.
- Markov Chain Monte Carlo methods; Metropolitan Hastings algorithms; the Gibbs sampler.
- Selected applications: e.g. kernel density; regression; design of experiment; time series.

- Desired learning outcomes (ability to...):
- Generate distributions by various methods.
- Use computer-intensive method for estimation and hypotheses testing.
- Conduct data analysis using one or more major statistical models.

- Cluster: Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Actuarial Science
- Nickname: Actuarial
- Credits: 3
- Grades: A-F
- Description: Basic concepts of risk theory and utility theory, applied calculus and probability models for the analysis of claims, frequency and severity of distributions, loss distributions, premium determinations, insurance with deductible, reinsurance , and self-insurance.
- Prerequisites: concurrent 4500 Theory of Statistics
- Crosslisted with: 5550 Basic Principles of Actuarial Science
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter course: 455 Basic Principles of Actuarial Science
- Sample textbook: Actex Study Manual for the SOA P / CAS 1, by Samuel A. Broverman, 2009 Ed. or ASM Study Manual for SOA P/Exam 1, by K. Ostaszewski,11th Ed. or Probability: The Science of Uncertainty with Applications to Investments, Insurance, and Engineering, by Michael A. Bean, 2001.
- Topics:
- Review of Algebra and Calculus.
- Review of Probability in the context of risk management (combinatorial techniques; moments; etc.)
- Frequently used distributions.
- Functions and transformations of random variables; mixtures and compound distributions.
- Insurance contracts with caps, deductibles, and coinsurance; life insurance and annuity contracts.

- Desired learning outcomes (ability to...):
- Find probabilities, moments and distributions using various methods.
- Solve the problems arising in the context of risk management.
- Be equipped with basic skills required for the first actuarial science exam.

- Cluster: Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Th of Interest & Life Con
- Nickname: Inter&Life
- Credits: 3
- Grades: A-F
- Description: Theory of interest and contingent payment models. Mathematical models for the actuarial present value of a future set of payments contingent on some random event(s); life insurance, life annuities, benefit reserves.
- Prerequisites: 4550 Basic Principles of Actuarial Science
- Crosslisted with: 5560 Theory of Interest and Life Contingencies
- Taught in: Spring
- Frequency: Sporadically
- Replaces the quarter course: 456 Theory of Interest and Life Contingencies
- Sample textbook: Mathematics of Investment and Credit (Fourth Edition), by S.A. Broverman, 2008. or The Theory of Interest (Third Edition), by S.G. Kellison, 2008. or K.Ostaszewski SOA FM/CAS Course 2 Study Aids, by K.Ostaszewski, 6th ed. 2009.
- Topics:
- Accumulation function and special cases of simple and compound interest.
- Nominal and effective interest and discount rates, and the force of interest.
- Present and accumulated values of a stream of cash flows; annuities.
- Determination of yield rates on investments, both portfolio and investment year methods.
- Determination of the time required to accumulate a given amount or repay a given loan amount.
- Amortization of lump sums, fixed income securities, depreciation, mortgages, etc.
- Application of interest theory to life contingency problems, net premiums and reserves.
- Life tables and life table functions; select and ultimate tables.
- Relationships between life table functions.
- Expected value of a future lifetime random variable.
- The probability distribution of a set of future cash flows contingent on a random event.
- Expected value and variance of future contingent cash flows, with assumed interest rate structure.
- Benefit premiums and reserves for individual life insurance and annuities, cost of a warranty.
- Managing Risk With Derivatives

- Desired learning outcomes (ability to...):
- Understand and calculate the time value of money.
- Calculate important characteristics for annuities, loans and bonds, based on given information.
- Analyze cash flows and portfolios.
- Conduct simply analysis and calculation for various financial derivatives.

- Cluster: Statistics + Actuarial

- Catalog Entry
- Abbreviated Title: Intro Numerical Analysis
- Nickname: NumAnal
- Credits: 3
- Grades: A-F
- Description: A survey of the ideas, methods, and algorithms in Numerical Analysis.
- Prerequisites: (3200 Applied Linear Algebra or 3210 Linear Algebra), 3400 Elementary Differential Equations, (3600 Applied Numerical Methods or CS 2300 or CS 2400 or ET 2100)
- Crosslisted with: 5600 Introduction to Numerical Analysis
- Taught in: Fall
- Frequency: Yearly
- Replaces the quarter courses: 444 Introduction to Numerical Analysis; 445 Advanced Numerical Methods; 446 Numerical Linear Algebra.
- Sample textbook: Numerical Analysis, Burden and Faires
- Topics:
- Floating point arithmetic
- numerical solution of systems of linear equations
- eigenvalues
- Iterative methods for solving nonlinear equations
- polynomial interpolation and approximations
- numerical differentiation and integration
- numerical solution of ordinary differential equations

- Desired learning outcomes (ability to...):
- Construct algorithms to solve mathematical problems based on a common set of strategies.
- Analyze the accuracy of such algorithms.
- Analyze the computational cost and efficiency of such algorithms.
- Identify the sources of failure of such algorithms, and avoid them.

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Wavelets & Applications
- Nickname: Wavelets
- Credits: 3
- Grades: A-F
- Description: An elementary introduction to Fourier and wavelet analysis and its applications in engineering, such as data analysis and signal and image analysis. Focus on understanding basic mathematical concepts and methodology, developing related numerical algorithms and their implementation using computer software such as Matlab wavelet toolbox. Prior experience with computer software and computer algebra systems, such as Matlab and basic computer programming skills are required.
- Prerequisites: 2302 Calculus II, (3200 Applied Linear Algebra or 3210 Linear Algebra), (3600 Applied Numerical Methods or CS 2300 or CS 2400 or ET 2100)
- Crosslisted with: 5610 Introduction to Waves and Wavelets with Applications
- Taught in: Fall
- Frequency: Every Second Year
- Replaces the quarter course: 448 Introduction to Waves and Wavelets with Applications
- Sample textbook: A Primer on Wavelets and Their Scientific Applications, Second Edition (Studies in Advanced Mathematics), James S. Walker, Chapman and Hall/CRC; January, 2008. ISBN-10: 1584887451, ISBN-13: 978-1584887454
- Topics:
- Haar wavelets
- Connection to theory of conservation and compaction of energy
- Multiresolution analysis
- Creating scaling signal and wavelets- 1D
- Daubechies wavelets
- Discrete Fourier Transform
- Frequency Description of Wavelets
- Application I: audio signal processing, compression and noise removal
- Wavelet toolbox and other software
- Wavelet transform in 2D
- Some topics in image processing
- Application II: Image compression using wavelet: fingerprint compression
- Creating scaling scaling signal and wavelets-2D

- Desired learning outcomes (ability to...):
- Understanding mathematical theory about conservation and compaction of energy, multiresolution analysis and the Fourier-wavelet connection
- developing ability to perform wavelet transform and discrete Fourier transform using computer software and basic wavelet-based problem solving techniques
- expanding knowledge about related numerical algorithms and their implementation

- Cluster: Analytic Undergraduate
- Notes: Rearrange prerequisites?

- Catalog Entry
- Abbreviated Title: Linear & Nonlinear Opt
- Nickname: LinNonOpt
- Credits: 3
- Grades: A-F
- Description: Solution methods, theory and applications of linear and nonlinear optimization problems. The focus is on the mathematics of efficient optimization algorithms, such as Simplex method and steepest ascent. Applications include production planning, financial models, network problems, game theory.
- Prerequisites: (3200 Applied Linear Algebra or 3210 Linear Algebra), 3300 Calculus III, (3600 Applied Numerical Methods or CS 2300 or CS 2400 or ET 2100)
- Crosslisted with: 5620 Linear and Nonlinear Optimization
- Taught in: Spring
- Frequency: Every Second Year
- Replaces the quarter course: 442 Theory of Linear and Nonlinear Programming
- Sample textbook: Introduction to Operations Research, by Frederick Hillier and Gerald Lieberman, eighth edition.
- Topics:
- Formulating linear and nonlinear programs for real-life problems
- Graphical method for solving linear programs
- Simplex method for solving linear programs
- Duality theory in linear programming
- Sensitivity analysis
- Interior-point methods
- Algorithms for solving nonlinear programs, such as steepest ascent
- Kuhn-Tucker conditions
- Quadratic programming
- Applications of linear and nonlinear programming

- Desired learning outcomes (ability to...):
- Students will know how to formulate real-life problems as linear and nonlinear programs, apply algorithms to solve the problems, understand the theory behind the solution methods which will help them to analyze the algorithms and design new ones.

- Cluster: Algebraic Undergraduate

- Catalog Entry
- Abbreviated Title: Discrete Modeling
- Nickname: ModelOptm
- Credits: 3
- Grades: A-F
- Description: Modeling and solving real-life problems by discrete optimization techniques. The discrete models include integer programming, dynamic programming, network optimization problems. Applications in large economic systems, scheduling, voting theory, telecom and transportation networks are discussed.
- Prerequisites: 3300 Calculus III
- Crosslisted with: 5630 Discrete Modeling and Optimization
- Taught in: Spring
- Frequency: Every Second Year
- Replaces the quarter course: 443 Mathematical Modeling and Optimization
- Sample textbook: Introduction to Operations Research, by Frederick Hillier and Gerald Lieberman, eighth edition.
- Topics:
- Modeling real-life situations as integer programs
- Modeling techniques using binary variables
- Branch-and-Bound method for solving integer programs
- Cutting Plane method for solving integer programs
- Dynamic programming
- Network optimization models
- Efficiency of algorithms
- Approximation algorithms

- Desired learning outcomes (ability to...):
- Students will know how to build optimization models using binary integer variables, dynamic programs, mathematical networks;
- apply algorithms to solve the optimization problems;
- analyze the algorithms in terms of their accuracy and efficiency;
- understand the theory behind the algorithms.

- Cluster: Algebraic Undergraduate
- Notes: prerequisite okay?

- Catalog Entry
- Abbreviated Title: Introduction to Topology
- Nickname: Topology
- Credits: 3
- Grades: A-F
- Description: Topology of Euclidean spaces and general metric spaces. Introduction to general topological spaces.
- Prerequisites: 4301 Advanced Calculus I
- Crosslisted with: 5700 Introduction to Topology
- Taught in: Spring
- Frequency: 3 out of 4 Years
- Replaces the quarter course: 480A,B Elementary Point Set Topology
- Sample textbook: R.Engelking, K.Sieklucki, Introduction to topology, Heldermann Verlag, Berlin, 1992. or J.R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975. or J.L.Kelley, General Topology, Springer-Verlag, New York-Berlin, 1975. or Elementary Topology Problem Textbook, by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf
- Topics:
- metric spaces
- Euclidean spaces as metric spaces
- open and closed sets in metric spaces
- convergent sequences
- limits and continuity
- compact and connected metric spaces
- continuous mappings and homeomorphisms between metric spaces
- the notion of a manifold
- examples of topological groups
- products of spaces.

- Desired learning outcomes (ability to...):
- formulate and prove generalizations of the Intermediate Value Theorem and the Extreme Value Theorem in the setting of metric spaces
- distinguish between homeomorphic and non-homeomorphic subsets of Euclidean spaces
- provide classification of compact 2-manifolds
- provide examples of convergent and divergent sequences in metric spaces
- recognize certain compact groups, such as groups of rotations of Euclidean spaces

- Cluster: Analytic Undergraduate

- Catalog Entry
- Abbreviated Title: Special Topics
- Credits: variable 1-3
- Grades: A-F, CR, PR
- Description: Selected topics not covered in regular offerings.
- Prerequisites: Permission of instructor and chair
- Taught in: Fall, Spring, Summer
- Frequency: Yearly
- Replaces the quarter course: 490 Special Topics
- Sample textbook: varies
- Topics:
- varies

- Desired learning outcomes (ability to...):
- Student will demonstrate mastery of the topic studied.

- Notes: May be repeated for credit.

- Catalog Entry
- Abbreviated Title: Studies in Mathematics
- Credits: 1-3
- Grades: A-F
- Description: Independent study of selected topics in mathematics studied under guidance of instructor with expertise and interest in field. (May be repeated for credit.)
- Prerequisites: 3300 Calculus III, 6 hours MATH 4200-4799, Jr. or Sr. status
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: 491 Studies in Math
- Sample textbook: Discretion of instructor; depending on topic.
- Topics:
- Varies depending on the discretion of instructor and student.

- Desired learning outcomes (ability to...):
- Student will gain expertise in a field of mathematics .

- Catalog Entry
- Abbreviated Title: Mathematics Research
- Credits: 2
- Grades: A-F
- Description: An advanced student works together with a faculty member on a research project in a topic of mathematics of interest to both the student and faculty. The student and faculty member must agree upon a research plan before the student registers for the course. The course can be taken (twice) as a TIER III equivalent. The student will be expected to write results and progress reports and present a final presentaion on the project
- Grading Rubric: Work will be assessed and grades assigned primarily based on both oral and written reports on the research
- Prerequisites: (3050 Discrete Math or CS 3000), (3200 Applied Linear Algebra or 3210 Linear Algebra), 3300 Calculus III, 6 hours MATH 4200-4799, Jr. or Sr. status
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: Currently proposed course.
- Sample textbook: Discretion of instructor.
- Topics:
- Discretion of instructor.

- Desired learning outcomes (ability to...):
- Student will complete a research project in mathematics
- The student will gain proficiency in written and oral communication of mathematics and its applications.

- Notes: Repeatable for Tier III equivalency

- Catalog Entry
- Abbreviated Title: Undergraduate Math Seminar I
- Credits: 1
- Grades: A-F
- Description: Student participate in a weekly seminar on topics in mathematics that are beyond the material covered in our regular courses. During the first semester the student will develop a proposal for a topic of interest to be presented in the second semester.
- Grading Rubric: Work will be assessed and grade assigned based on participation and written topic proposal
- Prerequisites: (3050 Discrete Math or CS 3000), (3200 Applied Linear Algebra or 3210 Linear Algebra), 3300 Calculus III, 6 hours MATH 4200-4799, Jr. or Sr. status
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: New Course
- Sample textbook: Varies; depending of the selection of topics.
- Topics:
- Various; depending of the choice of the students and instructor.

- Desired learning outcomes (ability to...):
- Student will become familiar with various advanced topics in mathematics or applications of mathematics
- The student will develop an individual plan for further study and a seminar in a chosen topic. MATH 4993 and 4994 together are a Tier III equivalent.

- Notes: Together with 4994 this will be a Tier III equivalent.

- Catalog Entry
- Abbreviated Title: Undergraduate Math Seminar I
- Credits: 2
- Grades: A-F
- Description: Student participate in a weekly seminar on topics in mathematics that are beyond the material covered in our regular courses. During the second semester the student will prepare and present a seminar and final report on a topic of interest. Together with 4993 this is a Tier III equivalent.
- Grading Rubric: Work will be assessed and grade assigned based primarily on the presentation and final report.
- Prerequisites: 4993 Undergraduate Mathematics Seminar I
- Taught in: Fall, Spring
- Frequency: Yearly
- Replaces the quarter course: New Course
- Sample textbook: Varies; depending of the selection of topics.
- Topics:
- Various; depending of the choice of the students and instructor.

- Desired learning outcomes (ability to...):
- Student will become familiar with various advanced topics in mathematics or applications of mathematics
- Student will complete an independent study of an advanced topic in mathematics or application of mathematics
- The student will gain proficiency in written and oral communication of mathematics and its applications.

- Notes: Together with 4993 this will be a Tier III equivalent.

This page was updated on Thu Feb 6 14:55:38 2014.