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Department of

Mathematics and Computer Science

Course Descriptions

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Mathematics Courses (MATH)

MATH 090 Intermediate Algebra
MATH 112 Investigations in Modern Mathematics
MATH 115 College Algebra
MATH 118 Essentials of Trigonometry
MATH 120 Introduction to Statistics
MATH 130 Survey of Calculus
MATH 150 Calculus I
MATH 151 Calculus II
MATH 160 Logic for Mathematics and Computer Science
MATH 200 Mathematical Concepts for Elementary Teachers I
MATH 250 Calculus III
MATH 300 Mathematical Concepts for Elementary Teachers II
MATH 305 Seminar in Teaching Mathematics
MATH 310 Applied Mathematics for Science and Engineering I
MATH 311 Applied Mathematics for Science and Engineering II
MATH 315 Applied Probability and Statistics
MATH 320 Linear Algebra
MATH 325W History of Mathematics
MATH 330 Ordinary Differential Equations
MATH 331 Partial Differential Equations
MATH 340 Numerical Analysis I
MATH 341 Numerical Analysis II
MATH 350 Probability
MATH 351 Mathematical Statistics
MATH 355 Combinatorics
MATH 360-361 Real Analysis I and II
MATH 365 Complex Function Theory
MATH 370 Theory of Numbers
MATH 375 Algebraic Systems
MATH 380 Geometry
MATH 385 Topology
MATH 388 Mathematical Logic
MATH 395 Mathematical Problem Solving Seminar
MATH 405 Advanced Perspective on High School Mathematics
MATH 445 Mathematical Modeling
MATH 494 Special Topics
MATH 495W Senior Project in Applied Mathematics A
MATH 496W Senior Project in Applied Mathematics B
MATH 498 Internship
MATH 499 Independent Study
Separator

Lower-Division Courses (math)

090 Intermediate Algebra / 3 UNITS
A survey of basic algebraic skills for students with insufficient mathematics preparation. This remedial course counts for “work-load credit” only. That is, its 3 units are counted as part of the student’s load during the semester in which it is taken, and the grade earned in the course is included in the computation of the student’s grade point average, but it does not satisfy any core curriculum requirement, or for the major or minor in mathematics, and it does not count toward the 124 units required for graduation. (every semester) Syllabus [PDF].

112 Investigations in Modern Mathematics / 3 UNITS
This core curriculum mathematics course provides a less algebraic alternative to MATH 115 for those students who need to fulfill the mathematical competency requirement, but who are not planning to go on in math. Topics may include: voting theory, graph theory, sequences, population growth, fractals, and recursion. Note 1: This course does not serve as a prerequisite to MATH 130, MATH 150, or MATH 200. Prerequisite: MATH 90 at USD with a grade of C- or better, or pass Level 1 mathematics placement exam within the previous year. (every semester) Syllabus [PDF].

115 College Algebra / 3 UNITS
Review of exponents, equations, and inequalities; function notation, composition, and inverses; linear, quadratic, polynomial, exponential, and logarithmic functions and their graphs. Prerequisite: MATH 090 at USD with a grade of C– or better, or pass Level 1 mathematics placement exam within the previous year. (every semester) Syllabus [PDF].

118 Essentials of Trigonometry / 1 UNIT
Definitions, solutions of right triangles, graphs, identities, and inverse trigonometric functions. (every semester) Syllabus [PDF].

120 Introduction to Statistics / 3 UNITS
Probability as a mathematical system, random variables and their distributions, confidence intervals, hypothesis testing, and other topics in statistical inference. Prerequisite: MATH 115 or equivalent. Syllabus [PDF].

130 Survey of Calculus / 3 UNITS
A terminal mathematics course giving an introduction to the concepts and techniques of elementary differential and integral calculus. Note 1: This course is not equivalent to MATH 150, and will not serve as a prerequisite to MATH 151. Prerequisite: MATH 115 with a grade of C– or better, or pass Level 2 mathematics placement exam within the previous year. (every semester) Syllabus [PDF].

150 Calculus I / 4 UNITS
Fundamental notions of analytic geometry, differential and integral calculus with elementary applications; historical references. Prerequisite: MATH 115 with a grade of C– or better, or Level 2 Math Placement Exam M-150 with a score of P. Students without a solid trigonometry background are strongly recommended to take MATH 118 prior to or concurrently with MATH 150. (every semester) Syllabus [PDF].

151 Calculus II / 4 UNITS
Continuation of Calculus I including integration, infinite series, differential equations, applications, and historical references. Prerequisite: MATH 150 with a minimum grade of C- or equivalent. (every semester) Syllabus [PDF].

160 Logic for Mathematics and Computer Science / 3 UNITS
Propositional calculus; first-order predicate calculus, mathematical proof, mathematical induction, fundamental set theory, relations and functions, and applications to problems in mathematics and computer science. Prerequisite: MATH 115, or pass Level 2 placement exam. This course satisfies the logic core curriculum requirement. (every semester) Syllabus [PDF].

200 Mathematical Concepts for Elementary Teachers I / 3 UNITS
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. It covers the mathematical content required by the California state teacher credentialing frameworks. Prerequisite: MATH 115 or equivalent. Syllabus [PDF].

250 Calculus III / 4 UNITS
Calculus of several variables, partial derivatives, multiple integration, elements of vector calculus, elements of differential equations, applications, and historical references. Prerequisite: MATH 151 with a minimum grade of C- or equivalent. (every semester) Syllabus [PDF].

Upper-Division Courses (MATH)

300 Mathematical Concepts for Elementary Teachers II / 3 UNITS
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. It covers the mathematical content required by the California state teacher credentialing frameworks. Prerequisite: MATH 200 or equivalent. Syllabus [PDF].

305 Seminar in Teaching Mathematics / 2 UNITS
Senior seminar for single subject credential students in mathematics. Contributions to mathematics by various ethnic, racial, and cultural groups by both men and women. Equity considerations in mathematics education. Variations in how students learn mathematics. Diverse methods of communication and assessment in mathematics. Practical aspects of teaching diverse students. Students will be required to do some tutoring in mathematics. This course is offered exclusively on a pass/fail basis. This course does not count toward the minor in mathematics or toward the upper-division mathematics electives of the mathematics major. Syllabus [PDF].

310 Applied Mathematics for Science and Engineering I / 3 UNITS
Matrix algebra, ordinary differential equations, and operational techniques. Prerequisite: MATH 151. Students may not take MATH 310 concurrently with MATH 330 or after having taken MATH 330. (spring semester, every year) Syllabus [PDF].

311 Applied Mathematics for Science and Engineering II / 3 UNITS
Boundary value problems, partial differential equations, Fourier methods, and introduction to complex analysis. Prerequisites: MATH 250 and 310. Students may not take MATH 311 concurrently with MATH 331 or after having taken MATH 331. (fall semester, every year) Syllabus [PDF].

315 Applied Probability and Statistics / 3 UNITS
Introduction to probability; discrete and continuous random variables; conditional and joint distributions and densities; functions of random variables; expectation and estimation; central limit theorem; introduction to statistics; introduction to random sequences and random processes. Prerequisite: MATH 250. (spring semester, every year) Syllabus [PDF].

320 Linear Algebra / 3 UNITS
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. Prerequisite: MATH 151 with a minimum grade of C- or consent of instructor. It is recommended that students take MATH 160 before taking MATH 320. (every semester) Syllabus [PDF].

325W History of Mathematics / 3 UNITS
Selected topics from the history of mathematics. The course will include a variety of writing assignments. Emphasis will be on the history of mathematical ideas, rather than on personalities or social background. Prerequisite: MATH 250 with a minimum grade of C-. (spring semester, even years) Syllabus [PDF].

330 Ordinary Differential Equations / 3 UNITS
Preliminary ideas, differential equations of the first and second order, linear equations with constant coefficients, operational techniques, simultaneous equations, series solutions, and applications. Prerequisite: MATH 250 with a minimum grade of C-. (fall semester, every year) Syllabus [PDF].

331 Partial Differential Equations / 3 UNITS
Preliminary notions, techniques for solving well-known partial differential equations of physics, orthogonal functions, and applications. Prerequisite: MATH 330 with a minimum grade of C-. Syllabus [PDF].

340 Numerical Analysis I / 3 UNITS
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 COMP 150 with a minimum grade of C-. Cross-listed as COMP 340. (spring semester, every year) Syllabus [PDF].

341 Numerical Analysis II / 3 UNITS
Estimation of eigenvalues and eigenvectors of matrices; numerical solutions of differential equations, existence, and stability theory; and computer lab assignments. Prerequisites: MATH 340 with a minimum grade of C-.

350 Probability / 3 UNITS
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 with a minimum grade of C- or consent of instructor. (fall semester, every year) Syllabus [PDF].

351 Mathematical Statistics / 3 UNITS
Statistical models, estimation, hypothesis testing, optimality, linear models, analysis of discrete data, and nonparametric methods. Prerequisite: MATH 350 with a minimum grade of C-. Syllabus [PDF].

355 Combinatorics / 3 UNITS
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 151 and 160 with a minimum grade of C-, or consent of instructor.

360-361 Real Analysis I and II / 3-3 UNITS
A study of the foundations of real analysis, including the calculus of functions of one and several variables, infinite processes, convergence theory, and selected topics of advanced undergraduate analysis. Prerequisites: MATH 160 and 250 with a minimum grade of C-. (360: fall semester, every year; 361: spring semester, odd years) Syllabus [PDF].

365 Complex Function Theory / 3 UNITS
Analytic function theory; power series, analytic continuation, conformal mapping, and applications. Prerequisite: MATH 160 and 250 with a minimum grade of C-, or consent of instructor.

370 Theory of Numbers / 3 UNITS
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 160 and 151, or consent of instructor. (spring semester, even years) Syllabus [PDF].

375 Algebraic Systems / 3 UNITS
An introduction to groups, rings, integral domains, division rings, fields, vector spaces, and algebras, and applications of these systems to other branches of mathematics. Prerequisites: MATH 160 and 151 with a minimum grade of C-, or consent of instructor. (spring semester, odd years)

380 Geometry / 3 UNITS
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 160 and 250 with a minimum grade of C-, or consent of instructor. (fall semester, odd years) Syllabus [PDF].

385 Topology / 3 UNITS
Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness. Prerequisites: MATH 160 and 250 with a minimum grade of C-, or consent of instructor. (spring semester, even years) Syllabus [PDF].

388 Mathematical Logic / 3 UNITS
Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic. Prerequisites: MATH 160 and 151 with a minimum grade of C-, or consent of instructor.

395 Mathematical Problem Solving Seminar / 1 UNIT
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. Prerequisite: MATH 151. (fall semester, every year)

405 Advanced Perspective on High School Mathematics / 3 UNITS
This course is a required course in the Mathematics Single Subject credential program. It provides a capstone experience for students in which they will 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.

445 Mathematical Modeling / 3 UNITS
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. Prerequisites: MATH 250, 320, and 330 with a minimum grade of C-, or consent of the instructor. (fall semester, every year) Syllabus [PDF].

494 Special Topics / 3 UNITS
Topics of special interest chosen by the instructor. May be repeated for credit with the consent of the instructor. Prerequisite: MATH 250 with a minimum grade of C- or consent of instructor.

495W Senior Project in Applied Mathematics A / 1 UNIT
Capstone senior project involving the application of mathematics to the solution of a problem or problems. Meets once per week: prepare a written research proposal for work to be carried out in MATH 496W; ongoing written and oral progress reports and regular consultation with the faculty supervisor. Prerequisites: MATH 445 with a minimum grade of C- (can be taken concurrently) and consent of the instructor. (fall semester, every year)

496W Senior Project in Applied Mathematics B / 2 UNITS
Capstone senior project involving the application of mathematics to the solution of a problem or problems. Meets twice per week: carry out the project defined in MATH 495W; ongoing written and oral progress reports and regular consultation with the faculty supervisor; final written and oral presentation in the presence of other students and faculty. Prerequisite: MATH 495W with a C– or better. (spring semester, every year)

498 Internship / 1-3 UNITS
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 3 units.

499 Independent Study / 3 UNITS
Student reading and research in selected special topics; student presentations. May be repeated for credit once with a different topic. Prerequisite: Consent of instructor.

Computer Science Courses

COMP 100 Introductory Computer Programming
COMP 150 Computer Programming I
COMP 151 Computer Programming II
COMP 160 Programming Languages
COMP 280 Introduction to Assembly Language
COMP 285 Data Structures and Algorithms
COMP 300 Principles of Digital Hardware
COMP 305 Object-oriented Design and Programming
COMP 310 Operating Systems
COMP 340 Numerical Analysis
COMP 345 Database Management Systems Design
COMP 350 Computer Graphics
COMP 355 Digital Modeling and Simulation
COMP 360 Principles of Programming Languages
COMP 370 Automata, Computability, and Formal Languages
COMP 375 Networking
COMP 380 Neural Networks
COMP 465W Software Engineering
COMP 480 Algorithms
COMP 494 Special Topics
COMP 495 Senior Project
COMP 498 Internship
COMP 499 Independent Study
Separator

Lower-Division Courses (COMP)

100 Introductory Computer Programming / 3 UNITS
An elementary introduction to computer programming and applications for non-majors and non-minors. Computer organization; problem solving; algorithms; structured programming in a simple computer language; computer applications; and current issues and trends in computer science. This course does not satisfy any of the requirements for the computer science major or minor and is not a substitute for COMP 150. (every semester) Syllabus [PDF].

150 Computer Programming I / 3 UNITS
Algorithms and programming in a selected computer language; expressions, statements, basic data types; sequence, decision, iteration; functions and procedures; arrays; recursion; file input and output; loop invariants; syntax analysis; and program design, documentation, validation, and debugging. Prerequisite: MATH 115 or equivalent. COMP 100 is not a prerequisite. (every semester) Syllabus [PDF].

151 Computer Programming II / 3 UNITS
Continuation of COMP 150. Basic data structures, including lists, stacks, queues, and binary trees; abstract data types; sorting and searching algorithms; exception handling; event driven programming; Prerequisite: COMP 150 with a minimum grade of C- or equivalent. (every semester) Syllabus [PDF].

160 Programming Languages / 3 UNITS
Introduction to a particular high-level programming language such as Ada, C, COBOL, Lisp, or Prolog. Programming assignments appropriate to the language studied. Prerequisite: COMP 150 with a minimum grade of C- or equivalent. This course does not satisfy any of the requirements for the major in Computer Science.

280 Introduction to Assembly Language / 3 UNITS
Machine structure; machine language; assembly language instructions and addressing modes; data representations; subroutines; macros; traps and interrupts; and input and output. Prerequisite: COMP 151 with a minimum grade of C-. (fall semester) Syllabus [PDF].

285 Data Structures and Algorithms / 3 UNITS
Data structures, algorithm analysis and general programming design and applications; balanced trees, hashing, priority queues, sets, and graphs; more on sorting and searching; Prerequisites: COMP 151 with a minimum grade of C- and MATH 160 with a minimum grade of C-, or equivalent courses. (fall semester) Syllabus [PDF].

Upper-Division Courses (COMP)

300 Principles of Digital Hardware / 4 UNITS
Combinational and sequential logic, registers, arithmetic units. Introduction to computer architecture. Three lectures and one laboratory per week. Prerequisites: COMP 280 with a minimum grade of C- and MATH 160 with a minimum grade of C-, or consent of instructor. (spring semester) Syllabus [PDF].

305 Object-oriented Design and Programming / 3 UNITS
Classes, encapsulation, inheritance, polymorphism, class derivation, abstract classes, namespaces, function overloading and overriding, function name overload resolution, container classes, template classes; unified modeling language (UML); constructing conceptual models, system sequence diagrams; design patterns; case studies. Prerequisite: COMP 151 with a minimum grade of C- or equivalent. (spring semester)

310 Operating Systems / 3 UNITS
Principles of computer operating systems; process management; memory management; file systems; protection; deadlock. Concurrent programming. Prerequisites: COMP 285 and 300 with a minimum grade of C-, or equivalent courses. (fall semester) Syllabus [PDF].

340 Numerical Analysis / 3 UNITS
Approximate computations and round-off errors; Taylor expansions; numerical solution of equations and systems of equations; systems of linear equations; numerical integration; numerical solution of differential equations; interpolation; and problem solving on the computer. Prerequisites: COMP 150 and MATH 151 with a minimum grade of C-. Cross-listed as MATH 340. (spring semester) Syllabus [PDF].

345 Database Management Systems Design / 3 UNITS
Introduction to database concepts; data models; query facilities; and file organization and security. Prerequisite: COMP 285 with a minimum grade of C-. Syllabus [PDF].

350 Computer Graphics / 3 UNITS
The development of high-level, device-independent graphics routines; basic line drawing algorithms, text design, and other graphics primitives; 2-D representations of coordinate systems, image segmentation, and windowing. Prerequisites: COMP 285 and MATH 151 with a minimum grade of C-. Syllabus [PDF].

355 Digital Modeling and Simulation / 3 UNITS
Mathematical modeling; probabilistic and deterministic simulations; pseudo-random number generators; event generators; queuing theory; game theory; and continuous models involving ordinary and partial differential equations. Prerequisites: COMP 305 and MATH 151 with a minimum grade of C-. Syllabus [PDF].

360 Principles of Programming Languages / 3 UNITS
The organization of programming languages with emphasis on language semantics; language definition, data types, and control structures of various languages. Prerequisite: COMP 285 with a minimum grade of C-; COMP 280 is recommended. Syllabus [PDF].

370 Automata, Computability, and Formal Languages / 3 UNITS
Finite state machines; formal grammars; computability and Turing machines. Prerequisites: COMP 285 with a minimum grade of C-, or upper-division mathematics course. (spring semester) Syllabus [PDF].

375 Networking / 3 UNITS
Introduction to the design and implementation of computer and communication networks. The focus is on the concepts and the fundamental design principles that have contributed to the global Internet’s success. Topics covered will include MAC layer design (Ethernet/802.11), the TCP/IP protocol stack, routing algorithms, congestion control and reliability, and applications (HTTP, FTP, etc.) and advanced topics such as peer-to-peer networks and network simulation tools. Recent trends in networking such as multimedia networking, mobile/cellular networks and sensor networks will also be discussed. Prerequisite: COMP 285 with a minimum grade of C- or equivalent.

380 Neural Networks / 3 UNITS
A study of the fundamental concepts, architectures, learning algorithms and applications of various artificial neural networks, including perceptron, kohonen self organizing maps, learning vector quantization, backpropagation, and radial basis functions. Prerequisites: COMP 285 and MATH 151 with a minimum grade of C-, or consent of instructor.

465W Software Engineering / 3 UNITS
Theoretical and practical aspects of software development; project planning; requirements and specification; general and detailed design; implementation; validation and verification; formal documentation. Students will participate in developing documentation for a large software project. Prerequisite: COMP 305 with a minimum grade of C-. (fall semester) Syllabus [PDF].

480 Algorithms / 3 UNITS
Advanced theory of algorithms. Topics may include: algorithm analysis; algorithm design techniques; and computational complexity. Prerequisites: COMP 285 and MATH 151 with a minimum grade of C-. Syllabus [PDF].

494 Special Topics / 3 UNITS
Topics of special interest chosen by the instructor. Prerequisites: COMP 305 with a minimum grade of C- and consent of the instructor. 494 may be repeated for credit with a different topic. Syllabus [PDF].

495 Senior Project / 2 UNITS
The course involves participation in a capstone senior project of substantial interest to computer scientists. Emphasis is on the design and implementation of computer systems for real problems. A final written report and oral presentation in the presence of other students and faculty are required. Prerequisites: COMP 465W with a minimum grade of C- and senior standing. (spring semester)

498 Internship / 1-3 UNITS
Practical experience in the application of the principles of computer science. Students will be involved in a software or hardware project. Enrollment is arranged on an individual basis according to the student’s interest, background, and the availability of positions. A written report is required. Units may not normally be applied toward the major or minor in Computer Science. COMP 498 may be repeated for a total of 3 units.

499 Independent Study / 1-3 UNITS
Individual study including library or laboratory research or program writing. A written report is required. Prerequisites: COMP 151 and consent of instructor. COMP 499 may be repeated for a total of 3 units.