Courses in Mathematics
Mathematics
MATH-B111 Mathematics for Business (3 cr)
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. Offered summer semester, occasionally.
- Prerequisite: HS Algebra 2 or Skills Review Test.
Credit given only for one: MATH-H111, MATH-E111, MATH-S111, or MATH-M123.
MATH-BE105 Math & Sci Combo (5 cr)
VT: CHEM-C105 / MATH-S122 For Science and Pre-Health professional majors. Not for students eligible for Pre-calculus. Registering for this course enrolls you in CHEM-C105 and MATH-S122.
MATH-E111 Mathematics for Elementary Education (3 cr)
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-H111, MATH-E111, MATH-S111, MATH-M123 or MATH-M110
- Prerequisite: HS Algebra 2 or Skills Review Test.
Open only to Elementary Education Majors
MATH-H111 Mathematics for the Humanities (3 cr)
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-H111, MATH-E111, MATH-S111, MATH-M123 or MATH-M110
- 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-L111 Mathematics Laboratory for Business, Social Science, Nursing (2 cr)
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 Fall and Spring semester.
MATH-N111 Mathematics for Nursing (3 cr)
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. Offered Summer semester, occasionally.
Credit given only for one: MATH-H111, MATH-E111, MATH-S111, MATH-M123 or MATH-M110
- Prerequisite: HS Algebra 2 or Skills Review Test.
Open only to Nursing students
MATH-S111 Mathematics for Social Sciences (3 cr)
Designed for the social science student to provide math skills in problem-solving and reasoning for application in social science professions. To develop problem-solving and reasoning skills, mathematics topics may include, but are not limited to: logic (statements and truth tables), algebra of equations and graphing, elementary statistics, set theory, and counting & probability. Emphasis will be placed on mathematical modeling and solving word problems.
Offered every Fall and Spring semester.
Credit given only for one: MATH-H111, MATH-E111, MATH-S111, or MATH-M123
- Prerequisite: HS Algebra 2 or Skills Review Test.
MATH-S122 College Algebra 1 (2 cr)
College Algebra 1 is the first course in a sequence with MATH-S123. With successful completion of both courses, the student will have algebraic skills and tools that are used for problem-solving in many professions. Topics will include but are not limited to linear, polynomial, rational, and radical equations, functions, and inequalities; solving, graphing, and evaluating; models and applications.
Offered every Fall semester.
- Prerequisite: HS Algebra 2 or Skills Review Test.
Credit given only for one: MATH-M123, MATH-E111, MATH-N111 MATH-B111, or MATH-S122
Must be taken concurrently with CHEM-C105 or other NSM designated course.
MATH-S123 College Algebra 2 (2 cr)
College Algebra 2 is the second course in a sequence with MATH-S122. With successful completion of both courses, the student will have algebraic skills and tools that are used for problem-solving in many professions. Topics will include but limited to linear, polynomial, rational, radical, exponential, and logarithmic equations, functions, and inequalities; solving, graphing, and evaluating; complex numbers; systems of equations and inequalities; matrices; models and applications. Offered every Spring semester.
- Prerequisite: MATH-S122.
Credit given for only one: MATH-M123, MATH-B111, MATH-N111, MATH-E111 or MATH-S123.
MATH-K300 Statistical Techniques (3 cr)
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.
MATH-M118 Finite Mathematics (3 cr)
Set theory, linear systems, matrices and determinants, probability, and linear programming. Applications to problems from business and the social sciences.
Offered every semester.
- Prerequisite: None
MATH-M119 Brief Survey of Calculus I (3 cr)
An introduction to calculus primarily for students in business and the social sciences. Credit not given for both MATH-M119 and MATH-M215.
Offered summer semesters.
- Prerequisite: Appropriate placement on skills review or MATH-M125 - Pre-calculus Mathematics.
MATH-M120 Brief Survey of Calculus II (3 cr)
A continuation of MATH-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 MATH-M216 and MATH-M120.
Offered periodically.
- Prerequisite: MATH-M119
MATH-M123 College Algebra (4 cr)
Designed to prepare you for MATH-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-L123 College Algebra Laboratory (2 cr)
Designed to prepare you for MATH-M125. Laboratory component to be taken concurrently with MATH-M123. (See course description above.) Not distribution satisfying.
Offered every semester.
- Co-requisite: MATH-M123.
MATH-M125 Pre-Calculus Mathematics (3 cr)
Designed to prepare you for MATH-M215. Algebraic operations; polynomial, exponential, and logarithmic functions and their graphs; conic sections; systems of equations; and inequalities.
Offered every semester.
- Prerequisite: None
MATH-M126 Trigonometric Functions (2 cr)
Designed to prepare you for MATH-M215. Trigonometric functions; identities. Graphs of trigonometric and inverse trigonometric functions.
Offered every semester.
- Prerequisite: MATH-M125 or equivalent (may be taken concurrently)
MATH-M215 Analytic Geometry and Calculus I (5 cr)
Coordinates, functions, straight lines, limits, continuity, derivatives, definite integral, applications, circles, conics, techniques of integration, and infinite series. Credit not given for both MATH-M119 and MATH-M215, or MATH-M120 and MATH-M216.
Offered every semester.
MATH-M216 Analytic Geometry and Calculus II (5 cr)
Coordinates, functions, straight lines, limits, continuity, derivatives, definite integral, applications, circles, conics, techniques of integration, and infinite series. Credit not given for both MATH-M119 and MATH-M215, or MATH-M120 and MATH-M216.
Offered every semester.
- Prerequisite: MATH-M215 or consent of instructor
MATH-M295 Readings and Research (1-3 cr)
Supervised problem solving.
Offered periodically.
- Prerequisite: Permission of a member of the mathematics faculty, who will act as supervisor.
MATH-M301 Applied Linear Algebra (3 cr)
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 MATH-M301 and MATH-M303.
Offered periodically.
- Prerequisite: MATH-M216 or consent of instructor
MATH-M303 Linear Algebra for Undergrads. (3 cr)
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 MATH-M301 and MATH-M303.
Offered fall and spring semesters.
- Prerequisite: MATH-M216 or consent of instructor
MATH-M311 Calculus III (3 cr)
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: MATH-M216 or consent of instructor
MATH-M312 Calculus IV (3 cr)
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: MATH-M311 or consent of instructor
MATH-M313 Elementary Differential Equations with Applications (3 cr)
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: MATH-M216 or consent of instructor.
MATH-M366 Elements of Statistical Inference (3 cr)
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, and occasionally spring.
- Co or Prerequisite: MATH-M215.
MATH-M371 Elem. Computational Methods (3 cr)
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.
- Prerequisite: MATH-M216, or consent of instructor.
MATH-M380 History of Mathematics (3 cr)
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: MATH-M215 or consent of instructor.
MATH-M393 Bridge to Abstract Mathematics (3 cr)
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 fall and spring semesters.
MATH-M403 Introduction to Modern Algebra I (3 cr)
Study of groups, rings, fields (usually including Galois theory), with applications to linear transformations.
Offered spring semesters.
MATH-M404 Introduction to Modern Algebra II (3 cr)
Study of groups, rings, fields (usually including Galois theory), with applications to linear transformations.
Offered periodically in summer semesters.
MATH-M405 Number Theory (3 cr)
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.
Offered summer semester.
- Prerequisite: MATH-M216 or consent of instructor.
MATH-M406 Topics in Mathematics (3 cr)
Selected topics in various areas of mathematics which are not covered by the standard courses. May be repeated for credit.
Offered periodically.
MATH-M413 Introduction to Analysis I (3 cr)
Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.
Offered fall semesters.
MATH-M414 Introduction to Analysis II (3 cr)
Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.
Offered periodically.
MATH-M421 Introduction to Topology I (3 cr)
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: MATH-M413
MATH-M422 Introduction to Topology II (3 cr)
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: MATH-M421
MATH-M447 Math Models & Applications I (3 cr)
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: MATH-M301 or MATH-M303, MATH-M311, MATH-M360 or MATH-M365, which may be taken concurrently or with consent of instructor.
MATH-M448 Math Models & Applications II (3 cr)
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 in spring semesters.
- Prerequisites: MATH-M447.
MATH-M451 The Mathematics of Finance (3 cr)
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 in the fall or summer semesters.
MATH-M463 Introduction to Probability Theory I (3 cr)
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.
Offered periodically in spring semesters.
MATH-M466 Introduction to Mathematical Statistics (3 cr)
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, the relationship of theory to practice.
No regular offerings.
- Prerequisite: MATH-M463 or consent of the instructor.
MATH-M499 Senior Seminar (3 cr)
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 fall and spring semester.
- Prerequisite: Senior standing as a Mathematics Major.
Mathematics for Educators
MATH-T321 Intuitive Topology (3 cr)
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 periodically.
- Prerequisite: MATH-M216 or consent of instructor.
MATH-T336 Topics in Euclidean Geometry (3 cr)
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 semesters, odd years.
- Prerequisite: MATH-M216 or consent of instructor.
MATH-J497 Internship in Teaching Collegiate Mathematics (1-3 cr)
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
MATH-M501 Survey of Algebra (3 cr)
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.
Open to Graduate-Level Students only or Consent of Instructor
MATH-M505 Basic Number Theory 1 (3 cr)
Congruencies, unites modulo n, lattices and abelian groups, quadratic residues, arithmetic functions, Diophantine equations, Farey fractions, continued fractions, partition function, the Sieve method, density of subsets of integers, c-function, the prime number theorem.
- Jointly offered with MATH-M405
Open to Graduate-Level Students only or Consent of Instructor
MATH-M511 Real Variables 1 (3 cr)
Sets and functions, cardinal and ordinal numbers, set functions, kinds of measures, integration, absolute continuity, convergence theorems, differentiation and integration.
Open to Graduate-Level Students only or Consent of Instructor
MATH-M512 Real Variables 2 (3 cr)
Normed linear spaces, function spaces, linear functionals, Banach spaces, Hilbert spaces, Fourier transforms, Schwartz class. Continuation of MATH-M511.
- Prerequisite: MATH-M511
Open to Graduate-Level Students only or Consent of Instructor
MATH-M521 Topology 1 (3 cr)
Point-set topology including connectedness, compactness, separation properties, products, quotients, metrization, function spaces.
- Prerequisite: MATH-M413
Open to Graduate-Level Students only or Consent of Instructor
MATH-M522 Topology 2 (3 cr)
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
Open to Graduate-Level Students only or Consent of Instructor
MATH-M551 Markets and Asset Pricing (3 cr)
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.
Open to Graduate-Level Students only or Consent of Instructor
MATH-M563 Theory of Probability I (3 cr)
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.
Open to Graduate-Level Students only or Consent of Instructor
MATH-M564 Theory of Probability II (3 cr)
Modes of convergence of sequences of random variables, ergodic theorems, Markov chains, and stochastic processes.
- Prerequisite: MATH-M563
Open to Graduate-Level Students only or Consent of Instructor
MATH-M571 Analysis of Numerical Methods I (3 cr)
Solution of systems of linear equations, elimination and iterative methods, error analyses, eigenvalue problems.
Open to Graduate-Level Students only or Consent of Instructor
MATH-M572 Analysis of Numerical Methods II (3 cr)
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
Open to Graduate-Level Students only or Consent of Instructor
MATH-T590 Seminar for Mathematics Teachers (3 cr)
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 cr)
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.
- Prerequisite: Open to MAT students only; Consent of 2 math faculty; Minimum GPA 3.0.
- Additional requirement: Teaching of a college level mathematics class