**MA 10000. An Introduction To Mathematical Sciences**

*(Class 1, Cr. 1)*

*Prerequisites: none.*

This course is intended to: integrate freshman mathematics majors into the department, help them adjust to university life, assist them in developing their academic and intellectual capabilities; introduces them to contemporary issues in mathematics, provide an overview of the careers open to those with degrees in mathematics. This course must be taken Pass/No Pass only. Credit by exam is not available for this course.

**MA 11500. Intermediate Algebra**

*(Class 3, Cr. 3)*

*Prerequisite: MA 02100 or a score of 016 College Level Mathematics CPI or 400 Math SAT or 400 ACT Math converted*

The purpose of this course is to strengthen and expand students’ basic algebraic skills and problem-solving capabilities and to prepare them for higher mathematics courses. For the purposes of general education requirements MA 11500 is not a collegiate level mathematics course, and therefore cannot be used to satisfy the general education requirement for mathematics at Purdue University Calumet.

**MA 13700. Mathematics For Elementary Teachers I**

(Class 3, Cr. 3)

*Prerequisites: A score of 83 Elementary Algebra or 400 Math SAT or 400 ACT Math converted*

Designed for prospective elementary school teachers. Problem solving. Numerical reasoning including self-generated and conventional algorithms. Whole and fractional number systems, elementary number theory. (At Purdue University West Lafayette, not available for credit in the School of Science.)

**MA 13800. Mathematics For Elementary Teachers II**

*(Class 3, Cr. 3)*

*Prerequisites: MA 13700 with a C or better*

Continues the study of number systems through integers, rational numbers and real numbers. Quantitative and proportional reasoning as a foundation for algebraic reasoning. Elementary statistical and probabilistic reasoning. (At Purdue University West Lafayette, not available for credit in the School of Science.)

**MA 13900. Mathematics For Elementary Teachers III**

*(Class 3, Cr. 3)*

*Prerequisites: MA 13700 with a C or better*

Geometric, measurement and spatial reasoning in one, two and three dimensions as the basis for elementary school geometry. Metric and non-metric geometry, transformation geometry. (At Purdue University West Lafayette, not available for credit in the School of Science.)

**MA 14700. Algebra And Trigonometry For Technology**

*(Class 3, Cr. 3)*

*Prerequisites: MA 04100 and MA 03100 or MA 11500 with a C- or better or College Level Math CPT of 51*

*(Not open to students with credit in MA 15100 or 15300.)*

MA 14700 and 14800 is a two semester sequence in algebra and trigonometry for students in technology. The emphasis is on technique and problem solving. MA 14700 concentrates on topics in algebra.

**MA 14800. Algebra And Trigonometry For Technology II**

*(Class 3, Cr. 3)*

*Prerequisites: MA 14700 with a C- or better or College Level Math CPT of 76*

*(Not open to students with credit in MA 15100, MA 15400, or MA 15900.)*

Continuation of MA 14700. MA 14800 concentrates on trigonometry.

**MA 15300. Algebra And Trigonometry I**

*(Class 3, Cr. 3)*

*Prerequisites: MA 03100 and MA 04100 or MA 11500 with a C- or better or College Level Math CPT 51*

*(Not open to students with credit in MA 14700, 14800, or 15100.)*

MA 15300 is College Algebra. The content of MA 15300, 15400 is similar to that of MA 15900 but the pace and emphasis is directed to students who do not intend to take MA 16300.

**MA 15400. Algebra And Trigonometry II**

*(Class 3, Cr. 3)*

*Prerequisites: MA 15300 with a C- or better or College Level Math CPT of 76*

*(Not open to students wit credit in MA 14800 or 15100.)*

MA 15400 is Trigonometry and is a continuation of MA 15300.

**MA 15900. Precalculus**

*(Class 5, Cr. 5)*

*Prerequisites: MA 03100 and MA 04100 or College Level Math CPT of 76*

Algebra and Trigonometry topics designed to prepare students for calculus.

**MA 16300. Integrated Calculus And Analytic Geometry I**

*(Class 5, Cr. 5)*

*Prerequisites: MA 15100 or MA 15900 with a C- or better or College Level Math CPT of 101*

Topics from plane analytic geometry. Introduction to differentiation and integration. Applications.

**MA 16400. Integrated Calculus And Analytic Geometry II**

*(Class 5, Cr. 5)*

*Prerequisites: MA 16300 with a C- or better*

Continuation of MA 16300. Completion of introductory study of topics in plane analytic geometry and the calculus of one variable, infinite series.

**MA 20500. Discrete Mathematics For Computer Technology**

*(Class 3, Cr. 3)*

*Prerequisites: MA 14700 or MA 15300 with a C- or better or College Level Math CPT of 76*

The course covers topics in discrete mathematics which are essential to the discipline of computer technology. These include: logic, sequences, mathematical introduction, basic set theory, functions, recursion, relations, graphs, and trees.

**MA 21400. Linear Algebra And Linear Programming**

*(Class 3, Cr. 3)*

Matrix algebra, systems of equations, topics from discrete mathematics.

**MA 21900. Calculus For Technology I**

*(Class 4, Cr. 4)*

*Prerequisites: MA 14800 with a C- or better or College Level Math CPT of 101*

*(Not open to students with credit in MA 16300, MA 22300 or MA 22500.)*

MA 21900 and 22200 is a two semester sequence in the techniques of calculus for student enrolled in certain technical curricula. MA 21900 develops topics from analytic geometry and introduces differentiation and integration differentiation. The offering pattern depends on the term offered.

**MA 22200. Calculus For Technology II**

*(Class 3, Cr. 3)*

*Prerequisites: MA 21900 or MA 22100 with a C- or better*

*(Not open to students with credit in MA 22400 or 16400.)*

Covers differentiation and integration of trigonometric, exponential, and logarithmic functions, infinite series, and first-order differential equations.

**MA 22300. Introductory Analysis I**

*(Class 3, Cr. 3)*

*Prerequisites: MA 15400 with a C- or better or College Level Math CPT of 101*

*(Students may not have credit in more than one of the following: MA 16300,
MA 22100, MA 22300 or MA 22500.)*

MA 22300 and 22400 form a two-course sequence and provide an introduction to the differential and integral calculus of one and several variables, and elementary differential equation, with applications to business, behavioral and biological sciences.

**MA 22400. Introductory Analysis II**

*(Class 3, Cr. 3)*

*Prerequisites: MA 22300 with a C- or better*

*(Not open to students with credit in MA 16400 or 22200.)*

Continuation of MA 22300.

**MA 22500. Calculus For Business And Mathematics**

*(Class 3, Cr. 3)*

*Prerequisites: MA 15300 with a C- or better or College Level Math CPT of 76*

*(Not open to students with credit in MA 16300, MA 22100 or MA 22300.)*

Functions and Limits. Differentiation and integration of algebraic functions of one variable. Applications of differentiation and integration.

**MA 26100. Multivariate Calculus**

*(Class 4, Cr. 4)*

*Prerequisites: MA 16400 with a C- or better*

Solid analytic geometry, partial differentiation, multiple integrals.

**MA 26400. Differential Equations**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26100 with a C- or better*

*(Not open to students with credit in MA 26200.)*

A first course in ordinary differential equations. First order differential equations, linear and nonlinear systems of differential equations, and second order differential equations.

**MA 26500. Linear Algebra**

*(Class 3, Cr. 3)*

*Prerequisites: MA 16400 with a C- or better*

*(Not open to students with credit in MA 26200.)*

An introduction to linear algebra. Systems of linear equations, matrix algebra, vector spaces, determinants, eigenvalues, eigenvectors, diagonalization of matrices, applications.

**MA 31200. Probability**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26100 with a C- or better*

A calculus-based introduction to0 probability theory and stochastic processes. Topics include probability spaces, random variables, distributions, expectation conditional probability, and discrete-state-space Markov chains.

**MA 31500. Introduction To Abstract Mathematics**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26100 with a C- or better*

This course is a bridge from the mainly computational mathematics courses to the upper-level abstract courses. It focuses on the development of students’ abilities to construct proofs, examples and counterexamples.

**MA 33000. Concepts in Geometry**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26100 with a C- or better*

Fundamental concepts in geometry. Euclidean, non-Euclidean (including spherical and hyperbolic geometry), and fractal geometry.

**MA 34800. Discrete Mathematics**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26500 with a C- or better*

A problem-centered introduction to topics in discrete mathematics including induction, permutations, combinations graphs, recurrence relations and generating functions.

**MA 35100. Elementary Linear Algebra**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26100 with a C- or better*

*(Not open to students with credit in MA 26500 or 35000.)*

Systems of linear equations, finite dimensional vector spaces, matrices, determinants, applications to analytical geometry.

**MA 40300. Mathematical Research**

*(Class 1 to 3, Cr. 1 to 3) Experiential Learning*

*Prerequisites: MA 26100 with a C- or better*

Undergraduate research in the mathematical sciences under the direction of a faculty member. May be used to fulfill an experiential learning requirement. Variable credit 1-3.

**MA 44600. Introduction Real Analysis**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26500 and MA 26400 and MA 31500 with a C- or better*

An introduction to basic concepts of real analysis. Topology of the real line, sequences, series, and various forms of convergence. Applications to derivatives and integrals.

**MA 45300. Elements Of Algebra**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26500 and MA 31500 with a C- or better*

The topics discussed are: fundamental properties of groups, rings, integral domains, fields; homomorphisms; Abelian groups and modules.

**MA 45400. Galois Theory**

*(Class 3, Cr. 3)*

*Prerequisites: MA 45300 with a C- or better*

Field extensions and automorphisms. Galois Theory.

**MA 47200. Introduction to Applied Mathematics**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26500 and MA 26400 and CS 20600 all with a C or better*

An introduction to the basic ideas and methods of applied mathematics. Topics taken from elementary partial differential equations, separation of variables and Fourier series, Fourier transforms, calculus of variations, applied linear algebra, numerical methods, modeling.

**MA 48000. The Practicum In Applied Mathematics**

*(Class 3, Cr. 3)*

The practicum course consists of a small team (a faculty advisor and 1-4 students) working on a real problem obtained in conjunction with a local business or industry. Not more then two terms of MA 48000 and/or CS 48000 may be taken for credit. (This course is the same as CS 48000.)

**MA 49000. Topics In Mathematics For Undergraduates**

*(Class 0 to 5, Cr.1 to 5)*

Supervised reading and reports in various fields. Open only to students with the consent of the department.

**MA 51000. Vector Calculus**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26400 and MA 26500*

*(Not open to students with credit in MA 36200.)*

Functions of several variables: partial derivative, differential; quadratic approximation, extrema; vector calculus, gradient; line, surface and volume integrals; divergence, curl, Laplacian, integral theorems; mappings, continuity, differentiability, inverse mapping; implicit functions; orthogonal coordinates.

**MA 52500. Introduction To Complex Analysis**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26400 or MA 26500*

Complex numbers and complex-valued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; elementary conformal mapping.

**MA 54000. Analysis I**

*(Class 3, Cr. 3)*

*Prerequisites: MA 44600*

Real number system, basic topology, infinite series, continuity, differentiation, integration.

**MA 54100. Analysis II**

*(Class 3, Cr. 3)*

*Prerequisites: MA 54000*

Sequences and series of functions, uniform convergence, equicontinuous families, the Stone-Weierstrass Theorem, Fourier series, introduction to Lebesgue measure and integration.

**MA 55300. Introduction To Abstract Algebra**

*(Class 3, Cr. 3)*

*Prerequisites: MA 45300*

Basic properties of groups, rings, integral domains, fields, polynomials Solvable groups. Finitely generated abelian groups. Algebraic and transcendental field extensions. Separable extensions. Normal extension, galois theory.

**MA 55400. Linear Algebra**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26500 and MA 31500*

Vector spaces, linear transformations, matrices. Solution of systems of linear equations. Determinant. Inner product spaces; orthogonal reduction of symmetric matrices. Direct sum decompositions, characteristic values, diagonal and nilpotent transformations, Jordan normal form.

**MA 55600. Introduction To The Theory Of Numbers**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26100*

Divisibility, congruences, quadratic residues, diophantine equations, the sequence of primes.

**MA 56000. Fundamental Concepts Of Geometry**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26100*

Foundations of Euclidean geometry, including Euclid’s elements and detailed study of an axiom system such as that of Hilbert. Independence of the parallel axiom and introduction to non-Euclidean geometry.

**MA 57100. Elementary Topology**

*(Class 3, Cr. 3)*

*Prerequisites: MA 44600*

General topological spaces and continuity. Connectedness. Separation. Compactness. Metric spaces. Function spaces.

**MA 58100. Introduction To Logic For Teachers**

*(Class 3, Cr. 3)*

*Prerequisites: MA 26200*

Sentential and general theory of inference and nature of proof; elementary axiom systems.

**MA 58300. History Of Elementary Mathematics**

*(Class 3, Cr. 3)*

A survey of elementary mathematics before calculus. will be made to link the history of mathematics to that of other sciences and to the social history of the relevant periods. Some acquaintance with ancient history of Europe is desirable.

**MA 58700. General Set Theory**

*(Class 3, Cr. 3)*

*Prerequisites: MA 45300 or MA 55000*

*Set algebra. Functions and relations. Ordering relations. Transfinite induction. Cardinal and ordinal numbers. The axiom of choice. Maximal principles. The continuum hypothesis. Application to algebra, analysis and topology.
*

**MA 59800. Topics In Mathematics**

*(Class 0 to 5, Cr. 1 to 5)*

*Directed study and reports for students who wish to undertake individual reading and study on approved topics.
*