**Major in Mathematical Sciences, Option 2: Applied Mathematics; 54-58 Credit Hours.**

MATH 165 - Calculus 1 (4)

MATH 166 - Calculus 2 (4)

MATH 215 - Discrete Systems (4)

MATH 217 - Linear Algebra (4)

MATH 259 - Introduction to Mathematical Software (3)

MATH 267 - Calculus 3 (4)

MATH 320 - Probability (4)

MATH 374 - Differential Equations (3)

MATH 411 - Abstract Algebra 1 (3)

MATH 471 - Real Analysis 1 (4)

MATH 498 - Senior Seminar (2)

**Option 2: Applied Mathematics 18-19 Hours**

MATH 335 - Mathematical Models (3)

MATH 362 - Numerical Analysis 1 (3)

**Two courses from two blocks (four courses total)**

**
Statistics **

MATH 321 - Mathematical Statistics (4)

MATH 422 - Theory of Sampling and Surveys (3)

MATH 428 - Regression and Time Series Models (3)

MATH 429 - Analysis of Variance in Experimental Design Models (3)

**
Discrete Mathematics **

MATH 412 - Abstract Algebra 2 (3)

MATH 415 - Mathematics of Coding and Communication (3)

MATH 416 - Theory of Numbers (3)

MATH 456 - Introduction to Operations Research (3)

**
Analysis **

MATH 363 - Numerical Analysis 2 (3)

MATH 377 - Complex Analysis (3)

MATH 472 - Real Analysis 2 (3)

MATH 473 - Boundary Value Problems (3)

MATH 475 - Topics in Partial Differential Equations (3)

Mathematical science students are encouraged to take CS 120 and PHYC 120. PHYC 120 satisfies the Tier 1 natural science requirement in the University Core Curriculum. Students are strongly advised to deepen their understanding of aspects of the program by selecting additional courses in areas such as business, computer science, finance, economics, or physics. By selecting additional courses appropriately, a student can earn a related minor in computer science, physics, or foundations of business for actuarial science and mathematics majors.

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**165 Calculus 1 (4)**

Differential calculus of algebraic and transcendental functions and applications, antidifferentiation and the Riemann integral. Includes the use of graphing calculators and computer software.

*Prerequisite: *C- or better in MATH 111 and MATH 112 or sufficient background in algebra and trigonometry as evidenced by the student's SAT/ACT scores and/or score on the mathematics placement test, or permission of the department chairperson.

**166 Calculus 2 (4)**

Standard techniques of integration, applications of the integral, sequences and series, indeterminate forms, and numerical methods. Includes the use of graphing calculators and computer software.

*Prerequisite: *MATH 165

**215 Discrete Systems (4)**

Topics from discrete mathematics, including formal logic, methods of proof, set theory, relations, recursion, combinatorics, and graph theory. A systematic development of number systems via equivalence classes is included as an application of these topics.

*Prerequisite: *MATH 162 or MATH 165 or permission of the department chairperson.

**217 Linear Algebra (4)**

Theory and application of systems of linear equations, vector equations, linear transformations, vector spaces, and inner product spaces. Includes the use of computer software.

*Prerequisite: *MATH 162 or MATH 165 or permission of the department chairperson.

**259 Introduction to Mathematical Software (3)**

Basic introduction to mathematical software currently used for solving math-related problems on computers. Includes a regularly scheduled computer laboratory.

*Prerequisite: *MATH 215 or permission of the department chairperson.

**267 Calculus 3 (4) **

Multidimensional calculus and its applications. Topics include three-dimensional vector calculus, Gauss's theorem, Green's theorem, and Stoke's theorem. Includes the use of graphing calculators and computer software.

*Prerequisite: *MATH 166

**320 Probability (4)**

Probability theory for discrete and continuous sample spaces, random variables, density functions, distribution functions, marginal and conditional distributions, mathematical expectation, moment-generating functions, common distributions, sampling distribution theory, central limit theorem, t, chi-square, and F distributions.

*Prerequisite:* MATH 166 or permission of the department chairperson.

*Parallel: *MATH 215.

**321 Mathematical Statistics (4)**

Point and interval estimation, maximum likelihood, Neyman-Pearson Lemma, likelihood ratio tests, classical tests of significance, goodness-of-fit, contingency tables, correlation, regression, nonparametric methods, Bayesian methods.

*Prerequisite: *MATH 320.

**335 Mathematical Models (3)**

Construction of mathematical models for use with problems in physics, chemistry, biology, and economics. Emphasizes the construction and interpretation of models. Existing computer software will be used.

*Prerequisite or parallel: *MATH 166 and MATH 217.

**362 Numerical Analysis 1 (3) **

Topics include error analysis, locating roots of equations, interpolation, numerical differentiation and integration, spline functions, smoothing of data. Includes programming of numerical algorithms.

*Prerequisite: *MATH 162 or MATH 166; and MATH 259 or CS 120; or permission of the department chairperson.

**363 Numerical Analysis 2 (3)**

Topics include direct and iterative methods for solving systems of linear equations, eigenvalue problems; minimization of functions and linear programming. Includes programming of numerical algorithms.

*Prerequisite: *MATH 217 and MATH 362; or permission of the department chairperson.

**374 Differential Equations (3)**

Introduction to nth-order ordinary differential equations, equations of order one, elementary applications, linear equations with constant coefficients, nonhomogeneous equations, undetermined coefficients, variation of parameters, linear systems of equations, and the Laplace transform. Use of standard computer software.

*Prerequisite: *MATH 162 or MATH 166 or permission of the department chairperson.

**377 Complex Analysis (3)**

Algebra and geometric representation of complex numbers, properties of complex analytic functions, contour integration, power series and Laurent series, poles and residues, conformal mapping, and applications.

*Prerequisite: *MATH 267 or permission of the department chairperson.

**411 Abstract Algebra 1 (3)**

The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange's Theorem, quotient structures, homomorphisms, automorphisms, group actions, Sylow's Theorems, structure of finite abelian groups, generators, and relations.

*Prerequisite: *MATH 215 and MATH 217; or permission of the department chairperson.

**412 Abstract Algebra 2 (3)**

An introduction to the theory of rings, including integral domains, division rings, and fields. Quotient fields of integral domains. Homomorphisms, ideals, and quotient structures. Factorization in commutative rings. Polynomial rings and field extensions. Aspects of Galois theory.

*Prerequisite: *MATH 411 or permission of the department chairperson.

**415 Mathematics of Coding and Communication (3)**

Exploration of applications of number theory, group theory, and linear algebra to areas such as cryptography and error-correcting codes; applications of graph theory to resource allocation and route planning; other possible topics selected by the instructor.

*Prerequisite:* MATH 215 and MATH 217; or permission of the department chairperson.

**416 Theory of Numbers (3)**

Topics include the division algorithm; positional notation; divisibility; primes; congruences; divisibility criteria; the sigma, divisor, and phi functions; diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson; quadratic reciprocity.

*Prerequisite: *MATH 215 or permission of the department chairperson.

**422 Theory of Sampling and Surveys (3)**

Survey designs; simple random, stratified, cluster, and systematic sampling; ratio estimates; regression estimates; cost and variance functions.

*Prerequisite: *MATH 321 or its equivalent.

**428 Regression and Time Series Models (3)**

Addresses regression topics that include simple and multiple linear regression, polynomial regression, regression diagnostics, and forecasting. Introduces time series topics that include exponential smoothing, auto-regressive, integrated, moving average (ARIMA) models, and forecasting.

*Prerequisite: *MATH 321 or equivalent.

**429 Analysis of Variance in Experimental Design Models (3)**

Multivariate normal distribution; quadratic forms; linear models; simple random, randomized block, Latin squares, factorial, split-plot, balanced incomplete block design; analysis of covariance; confounding; multiple comparison tests.

*Prerequisite: *MATH 321 or its equivalent.

**456 Introduction to Operations Research (3)**

Optimization techniques of linear programming, dynamic programming, and integer programming. Optimal solutions of PERT-CPM networks. Optimal decision strategies.

*Prerequisite: *MATH 162 or MATH 166 and MATH 217; or permission of the department chairperson.

**471 Real Analysis 1 (4)**

Real and complex number systems: ordered sets, least upper bound property, fields, Archimedean property; Basic topology: cardinality, metric spaces, completeness, compactness, connectedness; Numerical sequences and series: convergence tests, upper-lower limits; Continuity: continuous functions, uniform continuity, Intermediate and Extreme Value Theorems; Differentiation: derivative, Mean Value Theorem, 1'Hospital's Rule, Taylor's Theorem.

*Prerequisite: *MATH 215 and MATH 267; or permission of the department chairperson.

**472 Real Analysis 2 (3)**

The Riemann-Stieltjes integral and Fundamental Theorem of Calculus. Sequences and series of functions. Differential calculus of functions of several variables. Inverse and implicit function theorems. Extremum problems. Lebesgue integration and comparison with the Riemann integral.

*Prerequisite: *MATH 471

**473 Boundary Value Problems (3)**

Fourier Series and integrals, heat and wave equations in one dimension, Laplace's equation in two dimensions, problems in higher dimensions, numerical methods of solving boundary value problems.

*Prerequisite: *MATH 374

**475 Topics in Partial Differential Equations (3) **

Classical solution techniques for linear PDEs. Topics include first-and second-order equations, method of characteristics, special functions, orthogonal polynomials, transforms, Green's functions, and fundamental solutions. A computer algebra system is utilized.

*Prerequisite: *MATH 267 and MATH 374; or permission of the department chairperson.

**498 Senior Seminar (2)**

Development of a broad, connected, contemporary perspective of mathematics and its applications. Includes a variety of readings, special lectures, and discussions. Each student will participate in a substantial project, presented both in oral and written forms.

*Prerequisite: *senior standing or permission of the department chairperson.

*Open only to *mathematical sciences majors.

Robert Bell Building (RB), room 465

Ball State University

Muncie, IN 47306