**Minor in Mathematics 23 - 25 Credit Hours:**

MATH 165 - Calculus 1 (4)

MATH 166 - Calculus 2 (4)

MATH 267 - Calculus 3 (4)

**4 Hours from:**

MATH 215 - Discrete Systems (4)

MATH 217 - Linear Algebra (4)

**7-9 Hours from**:

MATH 215 - Discrete Systems (4)

MATH 217 - Linear Algebra (4)

MATH 221 - Probability and Statistics (3)

MATH 251 - Introduction to Mathematics of Finance (2)

MATH 259 - Introduction to Mathematical Software (3)

MATH 311 - Algebraic Structures (3)

MATH 320 - Probability (4)

MATH 321 - Mathematical Statistics (4)

MATH 335 - Mathematical Models (3)

MATH 345 - Survey of Geometries (4)

MATH 362 - Numerical Analysis 1 (3)

MATH 363 - Numerical Analysis 2 (3)

MATH 374 - Differential Equations (3)

MATH 377 - Complex Analysis (3)

MATH 415 - Mathematics of Coding and Communication (3)

MATH 416 - Theory of Numbers (3)

MATH 441 - Geometry and Topology (3)

MATH 445 - Differential Geometry (3)

MATH 456 - Introduction to Operations Research (3)

MATH 460 - History of Mathematics (3)

MATH 471 - Real Analysis 1 (4)

MATH 472 - Real Analysis 2 (3)

MATH 473 - Boundary Value Problems (3)

MATH 475 - Topics in Partial Differential Equations (3)

MATH 497 - Student-Faculty Colloquium (1-6)

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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.

**221 Probability and Statistics (3)**

Elementary probability theory, random variables, discrete and continuous probability distributions. Theory and applications of descriptive and inferential statistics. Statistical software and graphing calculator use is integrated throughout the course.

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

**251 Introduction to Mathematics of Finance (2)**

Mathematical topics in finance as expected to be useful in financial decision-making in the future. Topics will include compound and simple interest, savings, mortgages, loans, equity, annuities, equations of value, yield rates, amortization, sinking funds, bonds, and current topics in finance as time permits. Emphasis will be on fundamental principles, calculations, and practical applications.

*Prerequisite: *MATH 111 and MATH 112 or sufficient background in algebra and trigonometry as evidenced by the student's SAT/ACT scores and/or scores on the mathematics placement test.

**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

**311 Algebraic Structures (3)**

Consideration of the basic algebraic structures; groups, rings, integral domains, and fields. Examples of these structures and elementary proof will be emphasized as will polynomials over rings, integral domains, and the fields of real and complex numbers.

*Prerequisite: *MATH 215 and MATH 217.

**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.

**345 Survey of Geometries (4)**

A comparative study of Euclidean and non-Euclidean geometries, their respective histories and technologies, and their applications in mathematics, the sciences, and modern life.

*Prerequisite: *MATH 166 and MATH 215 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.

**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.

**441 Geometry and Topology (3)**

Introduction to geometric topology, including piecewise linear structures, Euler's formula, surfaces and solids, knots, graphs, and other topics.

*Prerequisite: *MATH 217 and MATH 267; or permission of the department chairperson.

**445 Differential Geometry (3)**

Fundamentals of differential geometry, as an extensive study of curves and surfaces in 3-space. Includes the use of computer visualization and emphasizes the importance of differential geometry in areas like relativity theory and modern physics.

*Prerequisites: *MATH 217 and MATH 267; or permission of the department chairperson.

**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.

**460 History of Mathematics (3) **

The development of mathematics from prehistoric times to the seventeenth century. Topics may include number concepts and numeration, algebra, geometry, trigonometry, analytic geometry, and calculus.

*Prerequisite: *MATH 161 or MATH 165.

**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.

*Prerequisites: *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.

**497 Student-Faculty Colloquium (1-6)**

Participatory colloquium experience for motivated students. A contemporary topic of broad mathematical interest is chosen each semester. Each student is paired with a faculty member. These pairs work together to develop and present components of the semester-long course.

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

A total of 6 hours of credit may be earned.

Robert Bell Building (RB), room 465

Ball State University

Muncie, IN 47306