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Undergraduate Course DescriptionsCollage of Undergraduate Course Offerings Concepts

Mathematical Sciences

Course codes: MA, STAT

If you are majoring in this discipline, you may want to consider the Science and Engineering Research Semester. See information under Arts and Sciences (Part 3).

MA 009 Topics In Elementary Algebra Class 1, Cr. 0.
P: consent of math department. A continuation of selected topics in elementary algebra. Offered pass/not pass only. Repeatable, maximum three times.
MA 013 Topics in Intermediate Algebra Class 1, Cr. 0.
P: consent of math department. A continuation of selected topics in intermediate algebra. Offered pass/not pass only. Repeatable, maximum three times.
MA 091 Professional Practicum I Cr. 0.
P: Must be accepted for the program by the Cooperative Education coordinator. For Cooperative Education students only.
MA 092 Professional Practicum II Cr. 0.
P: 091. Authorized equivalent courses or consent of instructor may be used in satisfying course pre- and corequisites.
MA 093 Professional Practicum III Cr. 0.
P: 092. Authorized equivalent courses or consent of instructor may be used in satisfying course pre- and corequisites.
MA 094 Professional Practicum IV Cr. 0.
P: 93. Authorized equivalent courses or consent of instructor may be used in satisfying course pre- and corequisites.
MA 095 Professional Practicum V Cr. 0.
P: 94. Authorized equivalent courses or consent of instructor may be used in satisfying course pre- and corequisites.
MA 101 Mathematics for Elementary Teachers I Cr. 3.
P: 109 with a grade of C or higher or placement at or above the MA 113 level and one year of high school geometry. A teacher’s perspective of the mathematics of the elementary school curriculum; in particular, mathematical problem solving, sets, numeration, and operations on the whole numbers.
MA 102 Mathematics for Elementary Teachers II Cr. 3.
P: 101 with a grade of C or higher. A teacher’s perspective of the mathematics of the elementary school curriculum, including operations on the integers and rationals, probability, and statistics.
MA 103 Mathematics for Elementary Teachers III Cr. 3.
P: 102 with a grade of C or higher and one year of high school geometry. Geometry and measurement concepts appropriate for the elementary school curriculum, including metric and nonmetric properties of geometric figures, measurement, coordinate geometry, graphs, and real-world applications of geometry.
MA 109 Elementary Algebra Cr. 3.
Review of decimals, fractions, percents, and integers. Fundamentals of algebra, linear equations and inequalities, word problems, polynomials, factoring, graphs, exponents, quadratic equations, and rational expressions. No credit toward any degree at IPFW.
MA 113 Intermediate Algebra Cr. 3.
P: 109 with a grade of C or higher or placement by departmental exam. Rational equations, functions, graphs of lines, slope, equations of lines, systems of equations in two variables, absolute value equations and inequalities, distance formula and midpoint formula, radical expressions and equations, rational exponents, quadratic equations and functions and their graphs, applications, and exponential and logarithmic equations and functions and their graphs. No credit toward any degree at IPFW.
MA 149 Basic and College Algebra Cr. 5.
P: 109 with a grade of B or higher, or placement by departmental exam. A onesemester version of 113 and 153. Only 3 credits may be counted toward graduation in Arts and Sciences, Business and Management Sciences, or Public and Environmental Affairs.
MA 153 Algebra and Trigonometry I Cr. 3.
P: 113 with a grade of C or higher or placement by departmental exam. Review of algebraic operations, factoring, exponents, radicals and rational exponents, and fractional expressions. Linear and quadratic equations and modeling, problem solving, and inequalities. Graphs of functions and transformations, including polynomial, rational, exponential, and logarithmic functions with applications.
MA 154 Algebra and Trigonometry II Cr. 3.
P: 149 or 153 with a grade of C or higher or placement by departmental exam. Trigonometric functions and graphs, vectors, complex numbers, conic sections, matrices, and sequences.
MA 159 Precalculus Cr. 5.
P: 113 with a grade of B or higher or placement by departmental exam. Algebra and trigonometry topics designed to prepare students for calculus.
MA 163H Honors Integrated Calculus and Analytic Geometry I Cr. 5.
Honors equivalent of MA 165.
MA 164H Honors Integrated Calculus and Analytic Geometry II Cr. 5.
P: 163H with a grade of C or higher. Honors equivalent of MA 166; continuation of MA 163H.
MA 165 Analytic Geometry and Calculus I Cr. 4.
P: 154 or 159 with a grade of C or higher or placement by departmental exam. Introduction to differential and integral calculus of one variable, with applications. Conic sections.
MA 166 Analytic Geometry and Calculus II Cr. 4.
P: 165 with a grade of C or higher. Continuation of MA 165. Vectors in two and three dimensions. Techniques of integration, infinite series, polar coordinates, surfaces in three dimensions.
MA 168 Mathematics for the Liberal Arts Student Cr. 3.
P: 113 with a grade of C or higher or placement by departmental exam. A course for liberal arts students that shows mathematics as the language of modern problem solving. The course is designed around problems concerning management science, statistics, social choice, size and shape, and computer science. Applications in quality control, consumer affairs, wildlife management, human decision making, architectural design, political practices, urban planning, space exploration, and more may be included in the course.
MA 175 Introductory Discrete Mathematics Cr. 3.
P: 165 or 153 and CS 160; or MA 153 and EET 264 with a grade of C or higher in each course. Sets, logical inference, induction, recursion, counting principles, binary relations, vectors and matrices, graphs, algorithm analysis.
MA 213 Finite Mathematics I Cr. 3.
P: 149 or 153 with a grade of C or higher or placement by departmental exam. Basic logic, set theory. Elementary probability, Markov chains. Vectors, matrices, linear systems, elementary graph theory. Applications to finite models in the managerial, social, and life sciences; and computer science.
MA 227 Calculus for Technology I Cr. 4.
P: 154 or 159 with a grade of C or higher or placement by departmental exam. Functions, derivatives, integrals. Applications to problems in the engineering technologies.
MA 228 Calculus for Technology II Cr. 3.
P: 227 with a grade of C or higher. Continuation of 227. Further topics in differentiation and integration. Introduction to infinite series, harmonic analysis, differential equations, and Laplace transforms. Applications to problems in the engineering technologies.
MA 229 Calculus for the Managerial, Social, and Biological Sciences I Cr. 3.
P: 153 or 149 with a grade of C or higher or placement by departmental exam. Differential and integral calculus of one variable. Applications to problems in business and the social and biological sciences.
MA 230 Calculus for the Managerial, Social, and Biological Sciences II Cr. 3.
P: 229 with a grade of C or higher. A continuation of 229 covering topics in elementary differential equations, calculus of functions of several variables, and infinite series.
MA 261 Multivariate Calculus Cr. 4.
P: 166 with a grade of C or higher. Solid analytic geometry, vector calculus, partial derivatives, and multiple integrals.
MA 263 Multivariate and Vector Calculus Class 4, Cr. 4.
P: 166 with a grade of C or higher. This course is primarily for students majoring in mathematics, but is appropriate for students majoring in engineering and the physical sciences who want a stronger background in vector calculus than is available in MA 261. Geometry of Euclidean space; partial derivatives, gradient; vector fields, divergence, curl; extrema, Lagrange multipliers; multiple integrals, Jacobian; line and surface integrals; theorems of Green, Gauss, and Stokes.
MA 275 Intermediate Discrete Math Cr. 3.
P: 261 or 263. Formal logic, proof techniques, elementary number theory, mathematical induction, functions, recurrence relations, sets, combinatorics, elementary graph theory, and applications. Students may not count both MA 175 and MA 275 toward graduation.
MA 305 Foundations of Higher Mathematics Cr. 3.
P: 166 and 175 with a grade of C or higher. Fundamental concepts used in higher courses, including logic and proof techniques, set theory, functions and relations, cardinality, number systems, the real numbers as a complete ordered field, and Epsilon-delta techniques.
MA 314 Introduction to Mathematical Modeling Cr. 3.
P: One semester of calculus, and MA 175 or MA 275 with a grade of C or higher. This course is intended to be accessible to students outside the mathematical and physical sciences. Formulation of mathematical models for applications in the biological, physical, and social sciences. Discrete and continuous models employing random and nonrandom simulation will be studied, with projects selected to fit the background and interests of the students.
MA 321 Applied Differential Equations Cr. 3.
P: 228 with a grade of C or higher. Designed primarily for EET majors. Ordinary differential equations with emphasis on linear equations and their applications. Laplace transforms. Fourier series, and an introduction to partial differential equations and their applications. No credit for math majors.
MA 351 Elementary Linear Algebra Cr. 3.
P: two semesters of calculus with grades of C or higher. Linear transformations, finite dimensional vector spaces, matrices, determinants, systems of linear equations, and applications to areas such as linear programming. Markov chains and differential equations.
MA 363 Differential Equations Cr. 3.
P: 261 or 263, and 351 with grades of C or higher. First order differential equations, higher order linear differential equations, systems of first order equations, series solutions, integral transforms, introduction to partial differential equations: separation of variables, Fourier series, Sturm-Liouville equations.
MA 417 Mathematical Programming Cr. 3.
P: 261 or 263 and one of: 262, 351 or 511 with grades of C or higher. This course is appropriate for majors in engineering, computer science, and mathematics. Construction of linear programming models; the simplex methods and variants, degeneracy and uncertainty in linear programming, gradient methods, dynamic programming, integer programming, principles of duality; twoperson zero-sum, nonzero-sum, n-person, and cooperative games.
MA 418 Computations Laboratory for MA 417 Practice 2, Cr. 1.
P: CS 160 or CS 114; C: or P: 417. Implementation on digital computer of those appropriate algorithms created in class to solve mathematical programming problems.
MA 441 Real Analysis Cr. 3.
P: 305. The theory of functions of a real variable; continuity, theory of differentiation and Riemann integration, sequences and series of functions, uniform convergence, interchange of limit operations.
MA 453 Elements of Algebra Cr. 3.
P: 305 and 351. Fundamental properties of homomorphisms, groups, rings, integers, polynomials, fields.
MA 490 Topics in Mathematics for Undergraduates Cr. 1–5. (V.T.)
Supervised reading and reports on approved topics in various fields.

Dual Level, Undergraduate-Graduate

MA 510 Vector Calculus Cr. 3.
P: 261 or 263. Calculus of functions of several variables and of vector fields in orthogonal coordinate systems; optimization problems; the implicit function theorem; Green’s, Stokes’, and the Divergence theorems; applications to engineering and the physical sciences.
MA 511 Linear Algebra with Applications Cr. 3.
P: 351. Real and complex vector spaces; linear transformations; Gram- Schmidt process and projections; least squares; QR and LU factorization; diagonalization, real and complex spectral theorem; Schur triangular form; Jordan canonical form; quadratic forms.
MA 521 Introduction to Optimization Problems Cr. 3.
P: 510, and 351 or 511. Necessary and sufficient conditions for local extrema in programming problems and in the calculus of variations. Control problems, statement of maximum principles, and applications. Discrete control problems.
MA 523 Introduction to Partial Differential Equations Cr. 3.
P: 261 or 263 and 363. First-order quasi-linear equations and their application to physical and social sciences; the Cauchy-Kovalevsky theorem; characteristics, classification, and canonical form of linear equations: equations of mathematical physics; study of the Laplace, wave, and heat equations; methods of solution.
MA 525 Introduction to Complex Analysis Cr. 3.
P: 263, 441 or 510. Complex numbers and complex-valued functions of one variable; differentiation and contour integration; Cauchy’s theorem; Taylor and Laurent series; residues; conformal mapping; applications.
MA 540 Analysis I Cr. 3.
P: 441. Metric spaces, compactness and connectedness, sequences and series, continuity and uniform continuity, differentiability, Taylor’s Theorem, Riemann-Stieltjes integrals.
MA 541 Analysis II Cr. 3.
P: 540. Sequences and series of functions, uniform convergence, equicontinuous families, the Stone-Weierstrass Theorem, Fourier series, introduction to Lebesgue measure and integration.
MA 553 Introduction to Abstract Algebra Cr. 3.
P: 453. Group theory: Sylow theorems, Jordan-Holder theorem, solvable groups. Ring theory: unique factorization in polynomial rings, and principal ideal domains. Field theory: straightedge and compass constructions, roots of unity, finite fields, Galois theory, and solubility of equations by radicals.
MA 554 Linear Algebra Cr. 3.
P: 453. Review of basics: vector spaces, dimension, linear maps, matrices determinants, linear equations. Bilinear forms; inner product spaces; spectral theory; eigen values. Modules over a principal ideal domain; finitely generated abelian groups; Jordan and rational canonical forms for a linear transformation.
MA 556 Introduction to the Theory of Numbers Cr. 3.
P: 263 or 261. Divisibility, congruences, quadratic residues, Diophantine equations, the sequence of primes.
MA 560 Fundamental Concepts of Geometry Cr. 3.
P: 305. Foundations of Euclidean geometry, including a critique of Euclid’s Elements and a detailed study of an axiom system such as that of Hilbert. Independence of the parallel axiom and introduction to non-Euclidean geometry.
MA 571 Elementary Topology Cr. 3.
P. 441. Fundamentals of point-set topology with a brief introduction to the fundamental group and related topics; topological and metric spaces; compactness and connectedness; separation properties; local compactness; introduction to function spaces; basic notions involving deformations of continuous paths.
MA 575 Graph Theory Cr. 3.
P: 305 or 351. Introduction to graph theory with applications.
MA 580 History of Mathematics Cr. 3.
P: two semesters of calculus and MA 305 or permission of instructor. The origins of mathematical ideas and their evolution over time, from early number systems and the evolution of algebra, geometry, and calculus to 20th-century results in the foundations of mathematics. Connections between mathematics and society, including the role of applications in the development of mathematical concepts.
MA 581 Introduction to Logic for Teachers Cr. 3.
P: 351 or consent of instructor. Sentential and general theory of inference and nature of proof, elementary axiom systems.
MA 598 Topics in Mathematics Cr. 1–5. (V.T.)
Supervised reading courses as well as dual-level special topics courses are given under this number.

Statistics

STAT 125 Communicating with Statistics Cr. 3.
P: MA 109 with a grade of C or higher. An introduction to the basic concepts and methods in statistical reasoning that are commonly referenced in the print media. Topics include data collection methods, descriptive statistics, basic techniques of estimation, and theory testing. Students will analyze and interpret statistics relating to contemporary problems in politics, business, science and social issues.
STAT 240 Statistical Methods for Biology Cr. 3.
P: MA 149 or MA 153 with a grade of C or higher. An introduction to the basic concepts and methods in a statistical analysis, with emphasis on applications in the life sciences. Descriptive statistics, discrete and continuous distributions, confidence interval estimation, hypothesis testing, and contingency tables.
STAT 301 Elementary Statistical Methods I Cr. 3.
P: MA 149 or MA 153 or MA 168 with a grade of C or higher. Not open to majors in mathematics or engineering. Credit should be allowed in no more than one of STAT 301or 511. Introduction to statistical methods with applications to diverse fields. Emphasis on understanding and interpreting standard techniques. Data analysis for one and several variables, design of samples and experiments, basic probability, sampling distributions, confidence intervals and significance tests for means and proportions, correlation and regression. Software is used throughout.
STAT 340 Elementary Statistical Methods II Cr. 3.
P: 240, 301, ECON 270, PSY 201 (or equivalent), one semester statistics course with a grade of C or higher. Statistical methods of simple linear regression, multiple linear regression, experimental design, analysis of variance, and nonparametric analysis. One or more statistical computer programs will be used. Student projects required, typically using data from the student’s major. STAT 490 Topics in Statistics for Undergraduates Cr. 1–5. (V.T.) Directed study for students who wish to undertake individual reading on approved topics.

Dual Level, Undergraduate-Graduate

STAT 511 Statistical Methods Cr. 3.
P: two semesters of calculus with a grade of C or higher. Descriptive statistics; elementary probability; sampling distributions; inference, testing hypotheses, and estimation; normal, binomial, Poisson, hypergeometric distributions; one-way analysis of variance; contingency tables; regression.
STAT 512 Applied Regression Analysis Cr. 3.
P: 511 or 517 or 528 with a grade of C or higher. Inference in simple and multiple linear regression, residual analysis, transformations, polynomial regression, model building with real data, nonlinear regression. One-way and twoway analysis of variance, multiple comparisons, fixed and random factors, analysis of covariance. Use of existing statistical computer programs.
STAT 514 Design of Experiments Cr. 3.
P: 512 with a grade of C or higher. Fundamentals, completely randomized design; randomized complete blocks; latin square; multi-classification; factorial; nested factorial; incomplete block and fractional replications for 2n, 3n, 2m x 3n; confounding; lattice designs; general mixed factorials; split plot; analysis of variance in regression models; optimum design. Use of existing statistical programs.
STAT 516 Basic Probability and Applications Cr. 3.
P: MA 261 or MA 263 with a grade of C or higher. A first course in probability intended to serve as a background for statistics and other applications. Sample spaces and axioms of probability, discrete and continuous random variables, conditional probability and Bayes’ theorem, joint and conditional probability distributions, expectations, moments and moment generating functions, law of large numbers and central limit theorem. (The probability material in Course 1 of the Society of Actuaries and the Casualty Actuarial Society is covered by this course.)
STAT 517 Statistical Inference Cr. 3.
P: 516 with a grade of C or higher. A basic course in statistical theory covering standard statistical methods and their application. Estimation including unbiased, maximum likelihood and moment estimation; testing hypotheses for standard distributions and contingency tables; confidence intervals and regions; introduction to nonparametric tests and linear regression.
STAT 519 Introduction to Probability Cr. 3.
P: MA 510 with a grade of C or higher or C: MA 441. Algebra of sets, sample spaces, combinatorial problems, independence, random variables, distribution functions, moment generating functions, special continuous and discrete distributions, distribution of a function of a random variable, limit theorems.
STAT 528 Introduction to Mathematical Statistics Cr. 3.
P: 519 with a grade of C or higher. Distribution of mean and variance in normal samples, sampling distributions derived from the normal distribution, Chi square, t and F. Distribution of statistics based on ordered samples. Asymptotic sampling distributions. Introduction to multivariate normal distribution and linear models. Sufficient statistics, maximum likelihood, least squares, linear estimation, other methods of point estimation, and discussion of their properties. Cramer-Rao inequality and Rao-Blackwell theorem. Tests of statistical hypotheses, simple and composite hypotheses, likelihood ratio tests, power of tests.

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