# Courses in Mathematics

## Mathematics

### MATH-K 300 Statistical Techniques (3)

An introduction to statistics. Nature of statistical data; ordering and manipulation of data; measures of central tendency and dispersion; elementary probability. Concepts of statistical inference decision; estimation and hypotheses testing. Special topics discussed may include regression and correlation, analysis of variance, non-parametric methods. Credit given for only one of the following: MATH K300, MATH K310, PSY K300, PSY K310, ECON E270, SPEA K300.

*Offered every semester.**Prerequisite: MATH-M123 (M118 suggested)*

### MATH-B111 Mathematics for Business (3)

With successful completion of this course, the student will have algebraic skills and tools that are used for problem-solving in the business professions and be prepared for MATH-M118 (Finite Mathematics) and ECON-E270 (Statistics). The college algebra topics will include, but not be limited to the following: Solving equations, functions, and inequalities; solving systems of linear equations; graphing of equations and functions; interpreting graphs/tables/charts of equations and functions; performing algebraic operations on polynomial, rational, radical expressions in one/several variables; development of mathematical model from a word problem; application of these algebraic concepts and skills in business applications.

*Offered every Fall and Spring Semester.**Prerequisite: HS Algebra 2 or Skills Review Test.**Credit not given for both MATH-B111 and MATH-M123 or MATHN111.*

### MATH-E111 **Mathematics for Elementary Education **(3)

Designed for the elementary education student to develop skills in the use of numeration systems, number theory, set theory, logic, networks, systems of equations, and geometry. These skills will be useful in future teaching assignments and for passing the State of Indiana Praxis exam. The purpose of Math-E111 is to provide the students with knowledge of the concepts, theories, and procedures in the mentioned areas.

*Offered every Fall and Spring semester.**Credit given only for one: MATH-E111, MATH-H111, MATH-M110, MATH-T101, MATH-T103.**Prerequisite: HS Algebra 2 or Skills Review Test.**Open only to Elementary Education Majors*

### MATH-H111 Mathematics for the Humanities (3)

Designed for the humanities student to provide a variety of topics in mathematics, including, but not limited to: numeration systems; geometry; financial management; statistics; set theory. The course also provides a general, historical perspective of mathematics and development of practical application skills. Emphasis will be placed on mathematical modeling and solving word problems.

*Offered every Fall and Spring semester.**Credit given only for one: MATH-E111, MATH-H111, MATH-M110, MATH-T101, MATH-T103.**Prerequisite: HS Algebra 2 or Skills Review Test.**As of Fall 2013 this course replaces MATH-M110.**May use this course to FX a previously taken MATH-M110.*

### MATH-N111 Mathematics for Nursing (3)

With successful completion of this course, the student will have algebraic skills and tools that are used for problem-solving in the nursing profession and be prepared for NURS-H355 (Data Analysis) and the nursing math test. The college algebra topics will include, but not be limited to the following: Solving

equations, functions, and inequalities; solving systems of linear equations; graphing of equations and functions; interpreting graphs/tables/charts of equations and functions; solving direct/indirect variation and proportion equations; use of dimensional analysis; development of mathematical model from a word problem; application of these algebraic concepts and skills in nursing applications.

*Offered every Fall and Spring semester.**Prerequisite: HS Algebra 2 or Skills Review Test.**Credit not given for both MATH-B111 and MATH-M123 or MATHN111.**Open only to Nursing students*

### MATH-L111 Mathematics Laboratory for Business, Social Science, Nursing (2)

A mathematics laboratory course to be taken concurrently with MATH-B111 or MATH-N111. (See course description for MATH-B111 or MATH-N111.) Designed to prepare you for MATH-M118 and statistics. Not distribution satisfying.

*Offered every semester.**Co-requisite: MATH-B111 or MATH-N111.*

### MATH-X111 Topics in Mathematics for Non-Majors (1-3)

Designed to provide a variety of topics in mathematics, including, but not limited to: geometry; financial management; statistics; set theory; voting methods; celestial navigation; math of ancient

civilizations. The course also provides a general, historical perspective of mathematics and development of practical application skills. Emphasis will be placed on mathematical modeling and solving word problems.

*Offered periodically.**Prerequisite: HS Algebra 2 or Skills Review Test.**May be repeated with different topic.*

### MATH-M 118 Finite Mathematics (3)

Set theory, linear systems, matrices and determinants, probability, and linear programming. Applications to problems from business and the social sciences.

*Offered every semester.**Prerequisite: Appropriate placement on skills review or MATH-M123*

### MATH-M 119 Brief Survey of Calculus I (3)

An introduction to calculus primarily for students in business and the social sciences. Credit not given for both M119 and M215.

*Offered summer semesters.**Prerequisite: Appropriate placement on skills review or M125 - Pre-calculus Mathematics.*

### MATH-M 120 Brief Survey of Calculus II (3)

A continuation of M119 covering topics in elementary differential equations, calculus of functions of several variables, and infinite series. Intended for non-physical science students. Credit not given for both M216 and M120.

*Offered periodically.**Prerequisite: M119*

### MATH-M 123 College Algebra (4)

Designed to prepare you for M125. Algebraic operations; polynomial, exponential, and logarithmic functions and their graphs; conic sections; systems of equations; and inequalities.

*Offered every semester.**Prerequisite: Appropriate placement on skills exam*

### MATH-L 123 College Algebra Laboratory (2)

Designed to prepare you for M125. Laboratory component to be taken concurrently with M123. (See course description above.) Not distribution satisfying.

*Offered every semester.**Co-requisite: M123.*

### MATH-M 125 Pre-Calculus Mathematics (3)

Designed to prepare you for M215. Algebraic operations; polynomial, exponential, and logarithmic functions and their graphs; conic sections; systems of equations; and inequalities.

*Offered every semester.**Prerequisite: Appropriate placement on skills exam, or MATH-M123*

### MATH-M 126 Trigonometric Functions (2)

Designed to prepare you for M215. Trigonometric functions; identities. Graphs of trigonometric and inverse trigonometric functions.

*Offered every semester.**Prerequisite: M125 or equivalent (may be taken concurrently).*

### MATH-M 215 Analytic Geometry and Calculus I (5)

Coordinates, functions, straight lines, limits, continuity, derivatives, definite integral, applications, circles, conics, techniques of integration, and infinite series. Credit not given for both M119 and M215, or M120 and M216.

*Offered every semester.**Prerequisite: Appropriate placement on skills review or both M125 and M126.*

### MATH-M 216 Analytic Geometry and Calculus II (5)

Coordinates, functions, straight lines, limits, continuity, derivatives, definite integral, applications, circles, conics, techniques of integration, and infinite series. Credit not given for both M119 and M215, or M120 and M216.

*Offered every semester.**Prerequisite:**M215**or consent of instructor.*

### MATH-M 295 Readings and Research (1-3)

Supervised problem solving.

*Offered periodically.**Prerequisite: Permission of a member of the mathematics faculty, who will act as supervisor.*

### MATH-M 301 Applied Linear Algebra (3)

Emphasis on applications: systems of linear equations, vector spaces, linear transformations, matrices, simplex method in linear programming. Computer used for applications. Credit not given for both M301 and M303.

*Offered periodically.**Prerequisite: M216 or consent of instructor.*

### MATH-M 303 Linear Algebra for Undergraduates (3)

Introduction to theory of real and complex vector spaces. Coordinate systems, linear dependence, and bases. Linear transformations and matrix calculus. Determinants and rank. Credit not given for both M301 and M303.

*Offered fall and spring semesters.**Prerequisite: M216 or consent of instructor.*

### MATH-M 311 Calculus III (3)

Elementary geometry of 2, 3, and n-space, functions of several variables, partial differentiation, minimum and maximum problems, and multiple integration.

*Offered every semester.**Prerequisite: M216 or consent of instructor.*

### MATH-M 312 Calculus IV (3)

Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Green’s theorem, surface integrals, Stokes’s theorem. Applications.

*Offered periodically.**Prerequisite: M311*

### MATH-M 313 Elementary Differential Equations with Applications (3)

Ordinary differential equations of first order and linear equations of higher order with applications, series solutions, operational methods, Laplace transforms, and numerical techniques.

*Offered summer semesters.**Prerequisite: M216 or consent of instructor.*

### MATH-M 366 Elements of Statistical Inference (3)

Sampling distributions (chi-square, T and F distributions), order statistical decisions and inference. Hypothesis-testing concepts, Neyman-Pearson lemma, likelihood ratio tests, power of tests. Point estimation, method of moments, maximum likelihood, Cramer-Rao bound, properties of estimators. Regression, correlation, analysis of variance, non-parametric methods.

*Offered fall semesters of even years (2014, 2016, etc.).**Prerequisite: M360 or consent of instructor.*

### MATH-M 371 Elementary Computational Methods (3)

Interpolation and approximation of functions, solution of equations, numerical integration, and differentiation. Errors, convergence, and stability of the procedures. You will write and use programs applying numerical methods.

*Offered fall semesters of odd years (2013, 2015, etc.).**Prerequisite: M216 and CSCI C301 or equivalent, or consent of instructor.*

### MATH-M 380 History of Mathematics (3)

Brief study of the development of algebra and trigonometry; practical, demonstrative, and analytic geometry; calculus, famous problems, calculating devices; famous mathematicians in these fields and chronological outlines in comparison with outlines in the sciences, history, philosophy, and astronomy.

*Offered fall semesters.**Prerequisite: M215 or consent of instructor.*

### MATH-M 393 Bridge to Abstract Mathematics (3)

Preparation for 400 level math courses. Teaches structures and strategies of proofs in a variety of mathematical settings: logic, sets, combinatorics, relations and functions and abstract algebra.

*Offered spring semesters.**Prerequisite: M216 or consent of instructor.*

### MATH-M 403 Introduction to Modern Algebra I (3)

Study of groups, rings, fields (usually including Galois Theory), with applications to linear transformations.

*Offered spring semesters of even years.**Prerequisite: M301 or M303, M391 or consent of instructor.*

### MATH-M 404 Introduction to Modern Algebra II (3)

Study of groups, rings, fields (usually including Galois Theory), with applications to linear transformations.

*Offered periodically in summer semesters.**Prerequisite: M301 or M303, M391 or consent of instructor.*

### MATH-M 405 Number Theory (3)

Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruencies, primitive roots, diophantine equations, quadratic residues, and sums of squares.

*Prerequisite: M216 or consent of instructor.**Offered every other summer semester.*

### MATH-M 406 Topics in Mathematics (3)

Selected topics in various areas of mathematics which are not covered by the standard courses. May be repeated for credit.

*Offered periodically.*

### MATH-M 413 Introduction to Analysis I (3)

Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.

*Offered fall semesters.**Prerequisite: M301/M303, and M311, or consent of instructor.*

### MATH-M 414 Introduction to Analysis II (3)

Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.

*Offered periodically.**Prerequisite: M301/M303, and M311, or consent of instructor.*

### MATH-M 415 Elementary Complex Variables (3)

Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integrations, calculus of residues, conformal mapping. Application to physics. Offered periodically.

*Prerequisite: Math-M311 or Consent of Instructor*

### MATH-M 421 Introduction to Topology I (3)

Introduction to point set topology with emphasis on metric spaces. Continuity, Cartesian products, connectedness, compactness, completeness. Elements of homotopy theory, fundamental group and covering spaces, elementary homology theory, applications to simplicial complexes and manifolds.

*Offered periodically.**Prerequisite: M303 and M311*

### MATH-M 422 Introduction to Topology II (3)

Introduction to point set topology with emphasis on metric spaces. Continuity, Cartesian products, connectedness, compactness, completeness. Elements of homotopy theory, fundamental group and covering spaces, elementary homology theory, applications to simplicial complexes and manifolds.

*Offered periodically.**Prerequisite: M303 and M311*

### MATH-M 447 Mathematical Models and Applications I (3)

Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth.

*Offered fall semesters.**Prerequisites: M301 or M303, M311, M360 or M365, which may be taken concurrently or with consent of instructor.*

### MATH-M 448 Mathematical Models and Applications II (3)

Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth.

*Offered periodically.**Prerequisites: M447.*

### MATH-M 451 MATHEMATICS OF FINANCE (3)

Course covers probability theory, Brownian motion, Ito's Lemma, stochastic differential equations, and dynamitic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates.

*Offered periodically.**Prerequisites: M447.*

### MATH-M 463 Introduction to Probability Theory I (3)

The meaning of probability. Random experiments, conditional probability, independence. Random variables, expected values and standard deviations, moment generating functions, important discrete and continuous distributions. Poisson processes. Multivariate distributions, basic limit laws such as

the central limit theorem.

*No regular offerings.**Prerequisites: MATH-M303 and MATH-M311 or the consent of the instructor.*

### MATH-M 466 Introduction to Mathematical Statistics (3)

Rigorous mathematical treatment of problems in sampling and statistical inference. Possible topics include sufficient statistics, exponential distributions, monotone likelihood ratio, most powerful tests, minimum variance estimates, shortest confidence intervals, linear models, maximum likelihood,

simultaneous equations, and the relationship of theory to practice.

*No regular offerings.**Prerequisite: MATH-M463 or consent of the instructor.*

### MATH-M499 Senior Seminar (2)

Students integrate their study of mathematics and explore the connections within fields of mathematics and other disciplines. Students usually create a portfolio that showcases their understanding of the areas of study within mathematics and their applications outside of mathematics. Alternatives may include internships or other projects, as approved by advisor.

*Offered every spring.**Prerequisite: Senior standing as a Mathematics Major.*

## Mathematics for Educators

### MATH-T 321 Intuitive Topology (3)

Intuitive description of topology, including networks and maps, topological equivalence, classification of surfaces, spheres with handles, Jordan curve theorem, transformations, and fixed-point theorems. Offered summer of even years.

*Prerequisite: M216 or consent of instructor.*

### MATH-T 336 Topics in Euclidean Geometry (3)

Axiom systems for the plane; the parallel postulate and non-Euclidean geometry; classical theorem. Geometric transformation theory; vectors and analytic geometry; convexity; theory of area and volume. Offered summer of odd years.

*Prerequisite: M216 or consent of instructor.*

### MATH-J497 Internship in Teaching Collegiate Mathematics (1-3)

Designed to provide an opportunity for students to teach basic algebra and observe with discussion instructional techniques at the collegiate level in preparation for further career development in teaching at a post-secondary level.

*Prerequisite: Senior standing in Mathematics degree or Math Education degree; Consent of 2 math faculty; Minimum GPA 3.0.**Additional requirement: Teaching of a college level mathematics class*

## Graduate Courses

There are currently no scheduled offerings for the courses listed below.

### MATH-M501 Survey of Algebra (3)

A continuation for the undergraduate sequence of Modern Algebra.

Groups: Jordan-Holder theorem, Sylow theorems, Free Groups.

Rings: Ideals and Factor Rings.

Fields: Algebraic closure; separable and inseparable algebraic extensions; Galois theory; finite fields, insolvability of the quintic.

*Prerequisite: MATH-M403 and M404**or consent of instructor.*

### MATH-M511 Real Variables 1 (3)

Sets and functions, cardinal and ordinal numbers, set functions, kinds of measures, integration, absolute continuity, convergence theorems, differentiation and integration.

*Prerequisite: MATH-M413 and M414**or consent of instructor.*

### MATH-M512 Real Variables 2 (3)

Normed linear spaces, function spaces,linear functionals, Banach spaces, Hilbert spaces, Fourier transforms, Schwartz class.

*Continuation of MATH-M511**Prerequisite: MATH-M511**or consent of instructor.*

### MATH-M521 Topology 1 (3)

Point-set topology including connectedness, compactness, separation properties, products, quotients, metrization, function spaces.

*Prerequisite: MATH-M421**or consent of instructor.*

### MATH-M522 Topology 2 (3)

Elementary homotopy theory including fundamental group and covering spaces. Introduction to homology theory with applications such as the Brouwer Fixed Point theorem.

*Continuation of MATH-M521**Prerequisite: MATH-M521**or consent of instructor.*

### MATH-M551 Markets and Asset Pricing(3)

The concept of arbitrage and risk-neutral pricing are introduced within the context of dynamical models of stock prices, bond prices and currency exchange rates. Specific models include multi-period binomial models, Markov processes, Brownian motion and martingales.

*Prerequisite: MATH-M421**or consent of instructor.*

### MATH-M563 Theory of Probability I (3)

Basic concepts of measure theory and integration, axiomatic foundations of probability theory, distribution functions and characteristic functions, infinitely divisible laws and the central limit problem.

*Prerequisite: MATH-M413 and M463**or consent of instructor.*

### MATH-M564 Theory of Probability II (3)

Modes of convergence of sequences of random variables, ergodic theorems, Markov chains, and stochastic processes.

*Prerequisite: MATH-M563**or consent of instructor.*

### MATH-M571 Analysis of Numerical Methods I (3)

Solution of systems of linear equations, elimination and iterative methods, error analyses, eigenvalue problems.

*Prerequisite: MATH-M413-M414 and M447-M448**or consent of instructor.*

### MATH-M572 Analysis of Numerical Methods II (3)

Numerical methods for integral equations and ordinary differential equations; finite difference, finite element, and Galerkin methods for partial differential equations; stability of methods.

*Prerequisite: MATH-M571**or consent of instructor.*

### MATH-T590 Seminar for Mathematics Teachers (3)

A seminar course for students in the M.A.T. program. Emphasis on the interrelationship among mathematical topics, curriculum reform, professional growth, and classroom practice. Specific topic selected jointly with the instructor.

*Open only to M.A.T. students.*

### MATH-J597 Internship in Teaching Collegiate Mathematics (1-3)

Designed to provide an opportunity for students to teach 100 and 200 level undergraduate math courses and observe with discussion instructional techniques at the collegiate level in preparation for further career development in teaching at a post-secondary level.