Course Information
Below are the approved courses offered by the Department of Mathematics. Not all courses offered below will be available every semester. Make sure to check course offerings on the registration portal for each upcoming semester.
Course Descriptions
MATH 100
Fundamentals of Algebraic Reasoning
Units: 3
The goal of this course is to develop fundamental algebra skills and mathematical intuition in order to prepare students for mathematics courses that satisfy the mathematical reasoning and quantitative reasoning core requirements at USD. Students will build mathematical intuition by modeling real life situations using mathematical tools. Students will develop skills for solving algebraic equations, simplifying expressions, and solving problems. Students will investigate linear, polynomial, and rational expressions through the lenses of verbal, graphical, numerical, and algebraic representations.
MATH 110
Investigations in Mathematics
Units: 3
Mathematics is much more than calculation; it is an imaginative and creative endeavor that studies all sorts of patterns and structures, many of which are beautiful, intriguing, and applicable to the real world. This course will explore some surprising and rewarding mathematical ideas in areas that could include games, fractals, ciphers, elections, finance, risk measurement, the nature of infinity, or others. Along the way, students may confront issues that challenge their intuition, gain sharper analytical reasoning skills, and experience mathematical questions that have remained unsolved for hundreds of years. This course does not serve as a prerequisite to MATH 120,, MATH 133, MATH 150, or MATH 200. Prerequisites: MATH 100 or Math 150 with a minimum grade of C- or Level 1 Math Placement Exam with a score of P (1MTH) or Level 2 Math Placement Exam with a score of P (2MTH or 3MTH).
MATH 115
College Algebra
Units: 3
Algebra review. The study of functions and their graphs, including linear, exponential, logarithmic and polynomial functions. Compositions of functions; inverse functions, transformations of functions. Domain and range of functions. Solving equations, inequalities, and systems of equations. The course helps students develop mathematical reasoning skills, particularly algebraic reasoning. Students apply algebraic reasoning to solve problems, including applied problems. Prerequisites: MATH 100 with a minimum grade of C- or Level 1 Math Placement Exam with a score of P (1MTH) or Level 2 Math Placement Exam with a score of P (2MTH or 3MTH).
MATH 118
Essentials of Trigonometry
Units: 1
Definitions, solutions of right triangles, graphs, identities, and inverse trigonometric functions.
MATH 133
Business Calculus
Units: 3
This course provides an introduction to differential calculus in the context of business applications, and mathematical finance. Additional business applications of linear algebra as time allows. Students may not receive credit for both Math 133 and Math 130. This course is intended for students in the School of Business. Prerequisites: Passing the appropriate departmental placement test within the previous year or MATH 115 with a minimum grade of C-.
MATH 140
Introduction to Statistics
Units: 3
Probability as a mathematical system, random variables and their distributions, confidence intervals, hypothesis testing, and other topics in statistical inference. Prerequisites: MATH 115 or MATH 130 or MATH 150.
MATH 150
Calculus I
Units: 4
Fundamental notions of analytic geometry, differential and integral calculus with elementary applications; historical references. Prerequisites: MATH 115 with a grade of C– or better, or pass Level 2 mathematics placement exam (3MTH). Students without a solid trigonometry background are strongly recommended to take MATH 118 prior to or concurrently with MATH 150.
MATH 151
Calculus II
Units: 4
Continuation of Calculus I including integration, infinite series, differential equations, applications, and historical references. Prerequisites: MATH 150 with a grade of C- or better.
MATH 200
Mathematical Concepts for Elementary Teachers I
Units: 3
Problem solving, sets, numeration systems, a development of the whole number system, geometric figures, and computers. Note: This course does not count toward either the major or minor in mathematics. Prerequisites: MATH 115 or MATH 130 or MATH 133 or MATH 150 with a grade of C- or better.
MATH 250
Calculus III
Units: 4
Calculus of several variables, partial derivatives, multiple integration, elements of vector calculus, elements of differential equations, applications, and historical references. Prerequisites: MATH 151 with a grade of C– or better.
MATH 260
Foundations of Higher Mathematics
Units: 3
Mathematics is a creative endeavor based on reasoning, discovery and justification. In higher mathematics we explore, conjecture, and formally prove theorems about the behavior of abstract objects that model different aspects of reality. This course is an introduction and transition to the goals, tools, and subject matter of higher mathematics, including logic, the methods and structure of mathematical proof, mathematical induction, basic set theory, creative problem solving, and mathematical writing and communication. Students may not receive credit for taking both Math 260 and Math 262. Prerequisites: MATH 150.
MATH 262
Discrete Mathematics
Units: 3
This course introduces students to discrete mathematical structures, in contrast to the continuous ones studied in calculus. It also serves as a gateway to higher mathematics, which is a creative endeavor based on reasoning, discovery, and justification, using abstract objects to model different aspects of reality. Core topics of the course, which emphasize creative problem solving and algorithmic thinking, include sets and functions, graph theory, induction and recursion, and logic and proof, with additional topics selected from number theory, combinatorics and probability. Prerequisites: MATH 150 or Math 151 or Math 250
MATH 294
Special Topics in Mathematics
Units: 0.5 TO 4
Topics of special interest chosen by the instructor. Prerequisites: Math 151.
MATH 299
Lower Division Independent Study in Mathematics
Units: 1 TO 3
Independent lower division study of mathematics under the supervision of a member of the mathematics faculty.
MATH 300
Mathematical Concepts for Elementary Teachers II
Units: 3
Measurement concepts, development of the real number system, algebra, geometric mappings, probability, and statistics. Note: This course does not count toward either the major or minor in Mathematics. Prerequisites: MATH 200 with a grade of C or better.
MATH 305
Seminar in Teaching Mathematics
Units: 2
Senior seminar for single subject credential students in mathematics. Issues in mathematics education including: Contribution to mathematics by men and women of various ethnic, racial, and cultural groups; equity considerations in mathematics education; variations in how students learn mathematics; diverse methods of communication and assessment in mathematics; and practical aspects of teaching diverse students. Students will be required to do some tutoring in mathematics. This course does not count toward the minor in mathematics or toward the upper division mathematics electives of the mathematics major (even for the secondary education emphasis).
MATH 310
Applied Mathematics for Science and Engineering I
Units: 3
Matrix algebra, ordinary differential equations, and operational techniques. Students may not receive credit for both MATH 310 and MATH 330 (mutually exclusive). Prerequisites: MATH 151 with a grade of C- or better.
MATH 320
Linear Algebra
Units: 3
Systems of linear equations, matrix algebra and operations, vector spaces of three or more dimensions, linear independence, inner product spaces, linear transformations and their matrices, determinants, eigenvalues and eigenvectors, and brief introduction to canonical forms. Prerequisites: (Math 151 or Math 260 or Math 262) with a grade of C- or higher.
MATH 325
History of Mathematics
Units: 3
Selected topics from the history of mathematics. The course includes a variety of writing assignments. Emphasis is on the history of mathematical ideas, rather than on personalities or social background. Prerequisites: Math 250 and (Math 260 or Math 262). Depending on the choice of subject matter in a particular year, the prerequisite of Math 250 may be waivable; contact the instructor for more information.
MATH 330
Ordinary Differential Equations
Units: 3
Preliminary ideas, differential equations of the first and second order, linear equations with constant coefficients, operational techniques, simultaneous equations, series solutions, and applications. Prerequisites: Math 250 and (Math 260 or Math 262), each with a grade of C- or higher.
MATH 335
Numerical Analysis
Units: 3
Approximate computations and round-off errors, Taylor expansions, numerical solution of equations and systems of equations, numerical integration, numerical solution of differential equations, interpolation, and problem solving on the computer. Prerequisites: Math 151 and (Math 260 or Math 262) and COMP 110, each with a grade of C- or higher.
MATH 335
Numerical Analysis
Units: 3
Approximate computations and round-off errors, Taylor expansions, numerical solution of equations and systems of equations, numerical integration, numerical solution of differential equations, interpolation, and problem solving on the computer. Prerequisites: Math 151 and (Math 260 or Math 262) and COMP 110, each with a grade of C- or higher.
MATH 350
Probability
Units: 3
Probability axioms, conditional probability, discrete and continuous sample spaces, random variables and common distributions, jointly distributed random variables, and central limit theorem. Prerequisite: Math 250 and (Math 260 or Math 262), each with a grade of C- or higher.
MATH 355
Combinatorics
Units: 3
Principles of enumeration, finite difference calculus, generating functions, finite difference equations, principle of Inclusion and Exclusion, introduction to the theory of combinatorial graphs, and applications to computer science. Prerequisites: Math 260 or Math 262 with a grade of C- or higher.
MATH 360
Real Analysis
Units: 3
Analysis is the study of the foundations of calculus, including formal definitions of limits and convergence, and careful proofs of basic facts about numbers and functions. This course is an introduction to analysis of functions of one real variable. Prerequisites: Math 260 or Math 262 with a grade of C- or higher and MATH 151 with a grade of C- or higher.
MATH 365
Complex Analysis
Units: 3
Analytic function theory; power series, analytic continuation, conformal mapping, and applications. Prerequisites: Math 260 or Math 262 with a grade of C- or higher and MATH 250 with a grade of C- or higher.
MATH 370
Theory of Numbers
Units: 3
Divisibility, Euclidean algorithm, fundamental theorem of arithmetic, congruences, Fermat’s theorem, Euler’s function, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic residues, reciprocity law, and continued fractions. Prerequisites: Math 260 or Math 262 with a grade of C- or higher and MATH 151 with a grade of C- or higher.
MATH 375
Abstract Algebra
Units: 3
Abstract algebra is the study of operations like addition and multiplication that act on objects other than numbers, such as vectors, matrices, polynomials, functions, transformations, and symmetries. This course is an introduction to the basic structures of abstract algebra: groups, rings, and associated structures such as homomorphisms, issomorphisms, and quotients. Prerequisites: MATH 320 with a grade of C- or better.
MATH 380
Geometry
Units: 3
An introduction to an area of modern geometry. The specific topic will be chosen from the following: non-Euclidean geometry, differential geometry, projective geometry, or metric geometry, and historical references. Prerequisites: Math 260 or Math 262 with a grade of C- or higher and MATH 250 with a grade of C- or higher.
MATH 385
Topology
Units: 3
Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness. Prerequisites: Math 260 or Math 262 with a grade of C- or higher and MATH 250 with a grade of C- or higher.
MATH 388
Mathematical Logic
Units: 3
Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic. Prerequisites: Math 260 or Math 262 with a grade of C- or higher and MATH 151 with a grade of C- or higher.
MATH 395
Mathematical Problem Solving Seminar
Units: 1
This course is intended for students who enjoy the challenge of mathematical problems. This course differs from other mathematics courses which are focused on the theory and applications of a single branch of mathematics. It emphasizes problem-solving techniques, creative thinking, and exposition of skills in different areas of mathematics such as algebra, calculus, geometry, and number theory. (May be taken twice for credit.) Prerequisites: MATH 151 with a grade of C- or better.
MATH 405
Advanced Perspective on High School Mathematics
Units: 3
This course is a required course in the Mathematics Single Subject credential program. It provides a capstone experience for future mathematics high school teachers, in which they look at topics in high school mathematics from an advanced viewpoint. Connections between mathematics topics and between basic and more advanced mathematics will be emphasized. This course does not count toward the minor in mathematics or toward the upper division mathematics electives of the mathematics major (even for the secondary education emphasis).
MATH 410
Applied Mathematics for Science and Engineering II
Units: 3
Boundary value problems, partial differential equations, Fourier methods, and introduction to complex analysis. Prerequisites: (MATH 250 with a grade of C- or better and 310 with a grade of C- or better) or (MATH 250 with a minimum grade of C- and MATH 320 with a minimum grade of C- and MATH 330 with a minimum grade of C-). Students may not take MATH 311 concurrently with MATH 430 or after having taken MATH 430.
MATH 425
Forum
Units: 3
The goal of this capstone mathematics course is to improve the ability to communicate mathematics, both written and oral, to a general and technical audience. In the process, students are exposed to a broad range of topics from modern and classical mathematics, and increase their familiarity with the culture of mathematics. This course fulfills the Core requirements for advanced writing and oral communication. Prerequisites: Two courses: MATH 320 and (MATH 325 OR MATH 330 OR MATH 430 OR MATH 340 OR MATH 35 OR MATH 350 OR MATH 342 OR MATH 355 OR MATH 360 OR MATH 460 OR MATH 365 OR MATH 370 OR MATH 375 OR MATH 380 OR MATH 385 OR MATH 388 OR MATH 450).
MATH 425
Forum
Units: 3
The goal of this capstone mathematics course is to improve the ability to communicate mathematics, both written and oral, to a general and technical audience. In the process, students are exposed to a broad range of topics from modern and classical mathematics, and increase their familiarity with the culture of mathematics. This course fulfills the Core requirements for advanced writing and oral communication. Prerequisites: Two courses: MATH 320 and (MATH 325 OR MATH 330 OR MATH 430 OR MATH 340 OR MATH 35 OR MATH 350 OR MATH 342 OR MATH 355 OR MATH 360 OR MATH 460 OR MATH 365 OR MATH 370 OR MATH 375 OR MATH 380 OR MATH 385 OR MATH 388 OR MATH 450).
MATH 430
Partial Differential Equations
Units: 3
Preliminary notions, techniques for solving well-known partial differential equations of physics, orthogonal functions, and applications. Prerequisites: MATH 330 or MATH 310 with a grade of C- or better.
MATH 430
Partial Differential Equations
Units: 3
Preliminary notions, techniques for solving well-known partial differential equations of physics, orthogonal functions, and applications. Prerequisites: MATH 330 or MATH 310 with a grade of C- or better.
MATH 435
Topics in Applied Mathematics
Units: 3
This course varies each semester and covers interdisciplinary mathematical content beyond the standard curriculum. Prerequisites: MATH 262 and MATH 320 or permission of instructor.
MATH 435
Topics in Applied Mathematics
Units: 3
This course varies each semester and covers interdisciplinary mathematical content beyond the standard curriculum. Prerequisites: MATH 262 and MATH 320 or permission of instructor.
MATH 442
Mathematical Statistics
Units: 3
Statistical models, estimation, hypothesis testing, optimality, linear models, analysis of discrete data, and nonparametric methods. Prereq: MATH 350 with a grade of C- or better.
MATH 442
Mathematical Statistics
Units: 3
Statistical models, estimation, hypothesis testing, optimality, linear models, analysis of discrete data, and nonparametric methods. Prereq: MATH 350 with a grade of C- or better.
MATH 450
Mathematical Modeling
Units: 3
The construction and analysis of mathematical models, simplifying assumptions and testing strategies; topics chosen by the instructor in dimensional analysis, discrete and continuous dynamical systems, stochastic models, linear systems, optimization models, statistical methods, and graph theory. Prereq: MATH 250 with a grade of C- or better, MATH 320 with a grade of C- or better and MATH 330 with a grade of C- or better.
MATH 450
Mathematical Modeling
Units: 3
The construction and analysis of mathematical models, simplifying assumptions and testing strategies; topics chosen by the instructor in dimensional analysis, discrete and continuous dynamical systems, stochastic models, linear systems, optimization models, statistical methods, and graph theory. Prereq: MATH 250 with a grade of C- or better, MATH 320 with a grade of C- or better and MATH 330 with a grade of C- or better.
MATH 460
Topics in Analysis
Units: 3
Analysis is the study of the foundations of calculus, including formal definitions of limits and convergence, and careful proofs of basic facts about numbers and functions. This course is a continuation of Math 360. Prerequisites: MATH 360 with a grade of C- or better.
MATH 460
Topics in Analysis
Units: 3
Analysis is the study of the foundations of calculus, including formal definitions of limits and convergence, and careful proofs of basic facts about numbers and functions. This course is a continuation of Math 360. Prerequisites: MATH 360 with a grade of C- or better.
MATH 493
Math Education Field Experience
Units: 1 TO 3
The goal of this course is to provide students who are working towards a single subject credential in mathematics with a supervised field experience working with pre-college learners of mathematics. The students must not only work with students learning mathematics, they must also reflect on that experience. They will write a paper of at least five pages in length in which they reflect on their experience, including any lessons they have learned for their future as credentialed mathematics teachers. This course is only for students who are intending to become pre-college teachers of mathematics. Prerequisites: Junior Standing. At least one Mathematics course numbered 300 or above.
MATH 494
Special Topics in Mathematics
Units: 0.5 TO 4
Topics of special interest chosen by the instructor. May be repeated for credit with the consent of the instructor.
MATH 496
Directed Research
Units: 1 TO 3
Independent research directed by a faculty member. Prerequisites: Two mathematics courses numbered 320 and higher, one of which can be taken concurrently.
MATH 498
Internship
Units: 1 TO 3
Practical experience in the application of mathematics. Students will be involved in projects conducted by businesses, agencies, and institutions. Enrollment is arranged on an individual basis according to the student’s interest and background, and the availability of positions. A written report is required. Units may not normally be applied toward the major or minor in mathematics. MATH 498 may be repeated for a total of three units.
MATH 499
Independent Study
Units: 1 TO 3
Student reading in selected special topics; student presentations. May be repeated for credit once with a different topic. Only six units of Math 499 will count towards completion of the Mathematics major. Additional units of Math 499 will only count as units towards graduation. Prerequisites: consent of instructor.