Department of Mathematics

Chair and Professor: Stowe
Assistant Chair and Professor: Fisher

Professors: Egger, R. Hill, Kratz, Lang, Laquer, Wolper

Associate Professors: Ford, Hanin, L. Hill, Kriloff, Lay, Palmer

Assistant Professors: Chen, Gironella, Gryazin, Payne, Van Kirk

Visiting Assistant Professors: Li, Venema

Part-time Adjunct Faculty: Barclay, Chiddix, Christensen, Dewey, Engle, Finnigan, Furness, Jones, Judy, Mayes, Mines, Moon, Reed, Rude, Weaver, Wilde, Wilson

Professor Emeritus: Cresswell, Parker

The undergraduate programs in Mathematics have the following objectives:

1. Students in algebra courses develop the algebra skills needed in later courses.
2. Students in general education courses gain an understanding of mathematics as a language in which to express, define, and answer questions about the world.
3. Students in courses that serve the sciences and engineering, particularly calculus and linear algebra courses, develop technical skills, learn to apply mathematical tools, and develop an understanding of the mathematical basis for those tools.
4. Students in statistics courses develop an understanding of the basic concepts of probability and statistics and learn how to use statistical tools in real-life problems.
5. Education students with a mathematics teaching major or minor gain a basic understanding of several areas of mathematics, develop a sense for exploring mathematics, and learn to read, write, and present mathematics.
6. Mathematics majors become acquainted with the major branches of the discipline; learn to read and write mathematics; and develop the mathematical skills and general knowledge necessary for employment or for graduate work in mathematics or other fields.

Bachelor of Science in Mathematics

The Bachelor of Science program is designed to prepare students to take positions in industry, to pursue graduate training, or to enter the teaching profession. It allows some flexibility in course work which necessitates close cooperation with a mathematics department advisor who should be selected early in the student's career. It is assumed that all students registered in mathematics courses numbered 300 or above have learned (a) at least one computer language and (b) introductory material in abstract mathematics, as in MATH 287.

Required Courses:

C S 181         Introduction to Computer 
                  Science and Programming I           3 cr
MATH 287        Discrete Structures                   3 cr
MATH 326        Elementary Analysis                   3 cr
MATH 330        Linear Algebra                        3 cr
MATH 360        Differential Equations                3 cr
MATH g407       Modern Algebra                        3 cr
MATH g423       Introduction to Real Analysis         3 cr

Plus one of the following three courses:

MATH 327        Vector Analysis                       3 cr
MATH 352        General Statistics                    3 cr
MATH 362        Introduction to Complex Variables     3 cr

Plus 12 more credits of 400-level mathematics coursework, which includes completing two of the following sequences:

MATH g407-g408  Modern Algebra                        6 cr
MATH g423-g424  Introduction to Real Analysis         6 cr
MATH g441-g442  Introduction to Numerical Analysis    6 cr

MATH g450-g451  Mathematical Statistics               6 cr

Associate of Science in Mathematics

Students seeking an Associate of Science degree in Mathematics must complete the following:

General Education Goals for the 
  Bachelor of Science*                            variable

One of the two tracks described below. 

Track A is designed to provide the student with a broad overview 
of basic topics in mathematics. Track B is designed to provide the 
student with the lower-division coursework generally expected for 
a major or minor in mathematics.

Track A

MATH 123        Mathematics in Modern Society         3 cr
MATH 127        The Language of Mathematics           3 cr
MATH 130        Finite Mathematics                    4 cr
MATH 144        Trigonometry**                        2 cr
MATH 160        Brief Calculus                        4 cr
MATH 253        Introduction to Statistics            3 cr
C S 181         Introduction to Computer 
                  Science and Programming I           3 cr
TOTAL MATH CREDITS:                               20-22 cr

**MATH 144 may be waived given a sufficient score on the Mathematics 
Placement Exam or the Mathematics Sub-test of the ACT or SAT.

Track B

C S 181         Introduction to Computer
                  Science and Programming I           3 cr
MATH 170        Calculus I                            4 cr
MATH 175        Calculus II                           4 cr
MATH 275        Calculus III                          4 cr
MATH 287        Discrete Structures                   3 cr
Approved MATH electives                               3 cr
TOTAL MATH CREDITS:                                  21 cr
Electives to bring total to 64 cr                 variable
                                              TOTAL: 64 cr

*The number of credits required for the General Education requirements 
varies depending on the student's performance on proficiency or placement 
tests in English, foreign languages, and mathematics.

Mathematics Minor

Required Courses:

C S 181         Introduction to Computer
                  Science and Programming I           3 cr 
MATH 170        Calculus I                            4 cr
MATH 175        Calculus II                           4 cr
MATH 275        Calculus III                          4 cr
MATH 330        Linear Algebra                        3 cr
MATH 360        Differential Equations                3 cr

Plus any pair from:

MATH 326-327    Elementary Analysis, Vector Analysis  6 cr
MATH g407-g408  Modern Algebra                        6 cr
MATH g441-g442  Introduction to Numerical Analysis    6 cr
MATH g450-g451  Mathematical Statistics               6 cr

Mathematics Courses

All mathematics courses except MATH 015 have prerequisites. Students place into a course either by completing the prerequisite courses with a grade of C- or better (S in MATH 015 and 025) or by achieving appropriate scores on the ACT exam, SAT exam, or Compass mathematics placement exam. For placement purposes, prerequisite coursework or placement examinations must have been taken within the last seven years. See the Mathematics Department for further information.

Students must pass a course with a grade of C- or better before using that course as a prerequisite for another mathematics course.

MATH 015 Arithmetic/Pre-algebra 0 credits (3 credit equivalent). Arithmetic of integers and rational numbers. Decimals; introduction to variables; linear equations; problems involving rates, ratios, proportions and percentages. Graded S/U. F, S

<>MATH 025 Elementary Algebra 0 credits (3 credit equivalent). Variables and algebraic expressions. Absolute value; linear equations and inequalities and their applications; expansion and factorization of polynomials; rational expressions; radical expressions; the real number line; the Cartesian coordinate system and graphing of linear equations. Graded S/U. PREREQ: MATH 015 or equivalent. F, S, Su

MATH 108 Intermediate Algebra 3 Credits. Topics in algebra, with an emphasis on solving equations and inequalities. Systems of linear equations; quadratic equations and the quadratic formula; polynomial, absolute value, rational, and radical equations and inequalities. Rational exponents; calculations and equations involving exponentials and logarithms. PREREQ: MATH 025. F, S, Su

MATH 123 Mathematics in Modern Society 3 credits.  Survey of applications of mathematics to real-world problems. Topics from graph theory, management science, political science, statistics, geometry, and computer science. PREREQ: MATH 025. Satisfies Goal 3 of the General Education Requirements. F, S, Su

MATH 127 The Language of Mathematics 3 credits.  Introduction to the precise language used throughout mathematics. Development of skills including reading with comprehension, expressing mathematical thoughts clearly, reasoning logically, and employing common patterns of mathematical thought. PREREQ: MATH 025. Satisfies Goal 3 of the General Education Requirements. F

MATH 130 Finite Mathematics 4 credits.  Introduction to probability, linear systems, inequalities, and linear programming. Applications directed to non-physical science areas. PREREQ: MATH 108. Satisfies Goal 3 of the General Education Requirements. S

MATH 143 College Algebra 3 credits. Functions and their graphs. Notation, domain, range, composition, and inverses. Basic transformations of graphs. Polynomial, rational, exponential, and logarithmic functions and their graphs, with applications. Theory of polynomial functions and equations. PREREQ: MATH 108. F, S, Su

MATH 144 Trigonometry 2 credits. Circular functions and right triangle approaches to trigonometry. Graphs of trigonometric functions: amplitude, frequency, phase shift. Trigonometric identities, inverse functions, and equations. Introduction to vectors in the plane, polar coordinates, and polar representation of complex numbers. PREREQ: MATH 143. F, S, Su

MATH 147 Precalculus 5 credits.  A single one-semester course equivalent to College Algebra (MATH 143) plus Trigonometry (MATH 144). Credit cannot be granted in both MATH 143 and MATH 147, or in both MATH 144 and MATH 147. PREREQ: MATH 108. F, S

MATH 157 Structure of Arithmetic for Elementary School Teachers 3 credits. Development of number systems. Emphasis on principles, representations, and concept development. For elementary education majors. PREREQ: MATH 143. F, S, Su

MATH 160 Brief Calculus 4 credits.  Course in differential and integral calculus designed primarily for students in biological sciences, social sciences, business, education, and humanities. Credit cannot be granted in both MATH 160 and MATH 170. PREREQ: MATH 143. Satisfies Goal 3 of the General Education Requirements. F, S, Su

MATH 170 Calculus I 4 credits.  First course in the sequence 170, 175, 275. Real-valued functions of one real variable: limits, continuity, derivatives, integrals, applications. Credit cannot be granted in both MATH 160 and MATH 170. PREREQ: MATH 147 OR MATH 143/144. Satisfies Goal 3 of the General Education Requirements. F, S, Su

MATH 175 Calculus II 4 credits.  Second course in the sequence 170, 175, 275. Techniques of integration, trigonometric integrals, improper integrals. Applications of definite integrals. First- and second-order linear differential equations with constant coefficients. Sequences and series. Parametric curves in the plane, polar coordinates. PREREQ: MATH 170. F, S

MATH 230 Introduction to Linear Algebra 2 credits. Vector algebra and geometry in 3-space, systems of linear equations, real n-space, linear transformations, determinants, eigenvalues. PREREQ: MATH 143. F, S, Su

MATH 253 Introduction to Statistics 3 credits.  Descriptive statistics, probability, confidence intervals, and hypothesis testing for one and two parameters. Emphasis on applications to a wide variety of disciplines. PREREQ: MATH 108. Satisfies Goal 3 of General Education Requirements. F, S, Su, W

MATH 257 Structure of Geometry and Probability for Elementary School Teachers 3 credits. Topics from geometry, probability, and statistics. Emphasis on principles, representations, and concept development. For elementary education majors. PREREQ: MATH 157. F, S

MATH 275 Calculus III 4 credits. Third course in the sequence 170, 175, 275.  Multivariable calculus. Vector algebra and geometry. Functions of several variables. Differentiation. Optimization. Multiple Integrals. Parametric curves and surfaces. Line and surface integrals. Vector fields. Green's, Stokes', and divergence theorems. PREREQ: MATH 175. F, S

MATH 287 Discrete Structures 3 credits. An introduction to discrete structures. Material covered will include sets, propositions, proofs, functions and relations, equivalence relations, quantifiers, Boolean algebras, graphs. Cross-listed as C S 287. PREREQ: MATH 160 or MATH 170. F, S

MATH 326 Elementary Analysis 3 credits. Rigorous calculus on real line. Completeness, compactness and connectedness. Continuity, images of compact and connected sets. Series, uniform convergence. Differentiability, inverse functions, chain rule. Integration, fundamental theorem, improper integrals. PREREQ: MATH 275 and MATH 287. S

MATH 327 Vector Analysis 3 credits. Calculus of vector functions of several variables, derivative matrix, chain rule, inverse function theorem, multiple integration. Change of variables. Integrals over curves and surfaces. Green's, Stokes' and divergence theorems. Applications to physics. PREREQ: MATH 275. F

MATH 330 Linear Algebra 3 credits. Rigorous treatment of vector spaces and the relationship between linear transformations and matrices. Inner product spaces, eigenvectors, and selected topics. PREREQ: MATH 175 and MATH 287. F, S

MATH 343 Modern Geometry 3 credits. Planar Euclidian geometry. Rigid motions and symmetry in the plane. PREREQ: MATH 287 and either MATH 230 or MATH  330. F

MATH 344 Modern Geometry 3 credits. Transformation groups. Topics from hyperbolic, projective, and other geometries. PREREQ: MATH 343. S

MATH 352 General Statistics 3 credits. Probability, random variables, discrete and continuous distributions such as the Binomial, Poisson, Geometric, Hypergeometric, Normal, and Gamma, sampling distribution, point and interval estimation, hypothesis testing. PREREQ: MATH 175 or permission of instructor. F

MATH 355 Operations Research 3 credits. Deterministic problems in operations research oriented towards business. Includes linear programming, transportation problems, network analysis, PERT, dynamic programming, and elementary game theory. PREREQ: MATH 230 or MATH 130, or permission of instructor. AF

MATH 356 Operations Research II 3 credits. Probabilistic models oriented towards business are treated. Selections from stochastic processes, Markov chains, queuing theory, inventory theory, reliability, decision analysis and simulation. PREREQ: MATH 355. AS

MATH 360 Differential Equations 3 credits. Theory and applications of ordinary differential equations. PREREQ: MATH 175 and MATH 230;  MATH 275 recommended. F, S

MATH 362 Introduction to Complex Variables 3 credits. Introduction to the study of functions of a complex variable including the algebra and geometry of complex numbers, analytic functions, power series, integral theorems, and applications. PREREQ: MATH 326 or permission of instructor. D

MATH g407 Modern Algebra I 3 credits. Rings, fields, groups, algebras, and selected topics in abstract algebra. PREREQ: MATH 287 and MATH 330. F

MATH g408 Modern Algebra II 3 credits. Rings, fields, groups, algebras, and selected topics in abstract algebra. PREREQ: MATH 407.  S

MATH g421 Advanced Engineering Mathematics I 3 credits. Analysis of complex linear and nonlinear engineering systems using advanced techniques, including Laplace transforms, Fourier series and classical partial differential equations. Cross-listed as ENGR g421. PREREQ: MATH 360. F

MATH g422 Advanced Engineering Mathematics II 3 credits. Analysis of complex linear and nonlinear engineering systems using advanced techniques, including probability and statistics, advanced numerical methods and variational calculus. Cross-listed as ENGR g422. PREREQ: ENGR g421 or MATH g421. S

MATH g423 Introduction to Real Analysis I 3 credits. The real number system, limits, sequences, series and convergence; metric spaces; completeness; and selected topics on measure and integration theory. PREREQ: MATH 287, MATH 326, MATH 330 and MATH 360. F

MATH g424 Introduction to Real Analysis II 3 credits. The real number system, limits, sequences, series and convergence; metric spaces; completeness; and selected topics on measure and integration theory. PREREQ: MATH 423. S

MATH g435 Elementary Number Theory 3 credits. Diophantine equations, prime number theorems, residue systems, theorems of Fermat and Wilson, and continued fractions. PREREQ: MATH g407. D

MATH g441 Introduction to Numerical Analysis 3 credits. Introduction to numerical techniques for solving problems dealing with nonlinear equations, systems of linear equations, differential equations, interpolation, numerical integration, and differentiation. PREREQ: MATH 326, MATH 330, and MATH 360 or permission of instructor. F

MATH g442 Introduction to Numerical Analysis 3 credits. Extension of MATH g441 for students who wish to pursue more advanced techniques with emphasis on analysis. Typical topics covered include numerical methods applied to partial differential equations, integral equations, and in-depth treatment of topics covered in MATH g441. PREREQ: MATH g441. S

MATH g450 Mathematical Statistics I 3 credits. Probability, random variables, discrete and continuous distributions, order statistics, limit theorems, point and interval estimation, uniformly most powerful tests, likelihood ratio tests, chi-square and F tests, nonparametric tests. PREREQ: MATH 326. F

MATH g451 Mathematical Statistics II 3 credits. Probability, random variables, discrete and continuous distributions, order statistics, limit theorems, point and interval estimation, uniformly most powerful tests, likelihood ratio tests, chi-square and F tests, nonparametric tests. PREREQ: MATH g450. S

MATH g457 Applied Regression Analysis 3 credits. Simple and multiple linear regression, polynomial regression, diagnostics, model selection, models with categorical variables. PREREQ: MATH 352 or permission of instructor. D

MATH g458 Experimental Design 3 credits. The linear model for experimental designs, analysis of variance and covariance, block designs, factorial designs, nested designs, choice of sample size. PREREQ: MATH 352 or permission of instructor. D

MATH g459 Applied Multivariate Analysis 3 credits. Matrix computation of summary statistics, graphical analysis of multivariate procedures, multivariate normal distribution, MANOVA, multivariate linear regression, principal components, factor analysis, canonical correlation analysis. PREREQ: MATH 352 or permission of instructor. D

MATH g465 Partial Differential Equations 3 credits. Equations of the first and second orders, methods of solution, Laplace's equation, heat equation, and wave equation. Emphasis on applications in physical sciences and engineering. PREREQ: MATH 360, and MATH 326 or MATH g421. D

MATH g473 Introduction to Topology 3 credits. Metric spaces; convergence; notions of continuity; connected, separable and compact spaces. PREREQ: Permission of instructor. D

MATH g481 Special Problems 1-3 credits. Reading and conference in an area not usually covered by a regular offering. Individual work under the supervision and guidance of a professor whose specialty includes the chosen area. Open to seniors and graduate students in good standing and with consent of the instructor. May be repeated for up to 6 credits. D

MATH g491 Mathematics Seminar 1-3 credits. Advanced reading and discussion on selected topics in mathematics. May be repeated. PREREQ: 90 credits or equivalent. D

IDAHO STATE UNIVERSITY Academic Information  Contact: webmaster@isu.edu Revised: June 2004