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Mathematics
(Intermediate algebra is prerequisite to all mathematics courses.)
NOTE: Proof of completion of Entry-Level Mathematics requirement required for Mathematics 104, 118, 119, 120, 121, 122, 140, 150, 210, 211, and 250: Copy of ELM score or verification of exemption.
104. Trigonometry (2) I, II (CAN MATH 8)
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA.
Basic concepts of analytic trigonometry.
118. Topics in Mathematics (3) (CAN MATH 2)
Prerequisites: Satisfaction of Entry-Level Mathematics requirement
and qualification on the Mathematics Departmental Placement Examination, Part IA.
Topics selected from algebra, analysis, geometry, logic, probability, or statistics, designed to give student insight into structure of mathematical theories and their applications. Not open to students with credit in Mathematics 140 or higher numbered courses.
119. Elementary Statistics for Business (3) I, II, S
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA.
Measures of central tendency/variability, frequency distributions Probability; Bayes theorem; probability distributions including binomial, hypergeometric, normal sampling and distributions. Significance testing. Regression and correlation. Not open to students with credit in Mathematics 250. Students with credit or concurrent registration in the following lower division statistics courses other than Mathematics 250 will be awarded a total of four units for the two (or more) courses: Biology 215, Economics 201, Engineering 140, Mathematics 119, Political Science 201, Psychology 270, and Sociology 201.
120. Calculus for Business Analysis (3) I, II, S (CAN MATH 34)
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA.
Matrix algebra. Calculus including differentiation and integration. Graphing and optimization. Exponential and logarithmic functions. Multivariable calculus.
121. Calculus for the Life Sciences I (3) I, II (CAN MATH 30)
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA.
Basic concepts of differential calculus with life science applications. Not intended for physical science or engineering majors. Not open to students with credit in Mathematics 150.
122. Calculus for the Life Sciences II (3) I, II
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement; qualification on the Mathematics Departmental Placement
Examination, Part IA; and Mathematics 121.
A continuation of Mathematics 121 with topics from integral calculus and an introduction to elementary differential equations. Not open to students with credit in Mathematics 150.
140. College Algebra (3) I, II, S
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA.
Functional notation, mathematical induction, complex numbers, DeMoivre's theorem, inequalities, binomial theorem, determinants, etc. Not open to students with credit in Mathematics 150.
150. Calculus I (5) I, II, S (CAN MATH 18)
Prerequisites: Knowledge of algebra, geometry, and trigonometry
as demonstrated by either (1) satisfactory completion of Mathematics
104 and 140 at SDSU with grades of C or better; or (2) satisfaction of
the Entry-Level Mathematics requirement and qualification on the
Mathematics Departmental Placement Examination, Part P for Mathematics 140 and Part III for Mathematics 104. Appropriate combinations
of (1) and (2) are also acceptable.
Algebraic and transcendental functions. Continuity and limits. The derivative and its applications. The integral.
151. Calculus II (4) I, II, S (CAN MATH 20)
Prerequisite: Mathematics 150 with minimum grade of C.
Techniques and applications of integration. Improper integrals. Differential equations. Infinite series. Conic sections. Curves in parametric form, polar coordinates.
210. Structure and Concepts of Elementary Mathematics I (3) I, II
This course or its equivalent is required for students working toward a multiple subject credential in elementary education.
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA.
Number sense and operation concepts; estimation, mental arithmetic, and algorithms; geometric concepts; linear measurements; problem solving strategies.
211. Structure and Concepts of Elementary Mathematics II (3) I, II
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA; and Mathematics 210.
Patterns and functions; rational and real numbers; proportional reasoning; geometric relationships; continuation of measurement topics; problem solving strategies.
245. Discrete Mathematics (3) I, II, S
Prerequisite: Mathematics 122 or 151.
Logic, methods of proof, set theory, number theory, equivalence and order relations, counting (combinations and permutations), solving recurrence relations.
250. Basic Statistical Methods (3) I, II
Prerequisites: Satisfaction of the Entry-Level Mathematics requirement and qualification on the Mathematics Departmental Placement
Examination, Part IA.
Descriptive statistics: histogram, measures of central tendency and variability; sampling distributions. Estimation and hypothesis tests for means, proportions, variances, AOV models, linear regression and correlation, nonparametric methods. Not open to students with credit in Mathematics 119. Students with credit or concurrent registration in the following lower division statistics courses other than Mathematics 119 will be awarded a total of four units for the two (or more) courses: Biology 215, Economics 201, Engineering 140, Mathematics 250, Political Science 201, Psychology 270, and Sociology 201.
252. Calculus III (4) I, II, S (CAN MATH 22)
Prerequisite: Mathematics 151 with minimum grade of C.
Functions of several variables. Vectors. Partial derivatives and multiple integrals. Line integrals and Green's Theorem.
254. Introduction to Linear Algebra (3) I, II, S
Prerequisite: Mathematics 151.
Matrix algebra, Gaussian elimination, determinants, vector spaces, linear transformations, orthogonality, eigenvalues, and eigenvectors.
296. Experimental Topics (1-4)
Selected topics. May be repeated with new content. See Class Schedule for specific content. Limit of nine units of any combination of 296, 496, 596 courses applicable to a bachelor's degree.
299. Special Study (1-3)
Prerequisite: Consent of instructor.
Individual study. Maximum credit six units.
NOTE: Proof of completion of prerequisites required for all upper division courses: Copy of transcript.
302. Basic Mathematical Concepts (3) I, II
Prerequisite: Mathematics 150.
Concepts of secondary school mathematics from teacher's point of view to include mappings, relations, and operations topics from mathematical systems and number theory.
303. History of Mathematics (3) I, II
Prerequisites: Mathematics 104 and 140, or students using course
to satisfy General Education must complete the General Education
requirement in Foundations IIA., Natural Sciences and Quantitative
Reasoning.
Major currents in the development of mathematics from ancient Egypt and Babylon to late nineteenth century Europe.
312. Modern Elementary Mathematics I (3) I, II
Prerequisites: Mathematics 211 and qualification on Mathematics
Departmental Placement Examination, Part IA.
Topics in mathematics, selected from algebra, geometry, number theory, probability, statistics, logic, and mathematical systems; problem solving. Enrollment limited to future teachers in grades K-8.
313. Modern Elementary Mathematics II (3)
Prerequisite: Mathematics 312.
Continuation of Mathematics 312. Enrollment limited to future teachers in grades K-8.
336. Introduction to Mathematical Modeling (3) I
Prerequisite: Mathematics 254.
Models from the physical, natural, and social sciences including population models and arms race models. Emphasis on classes of models such as equilibrium models and compartment models.
337. Elementary Differential Equations (3) I, II
Prerequisite: Mathematics 151.
Integration of first-order differential equations, initial and boundary value problems for second-order equations, series solutions and transform methods, regular singularities.
342A. Methods of Applied Mathematics I (3) I, II
Prerequisite: Mathematics 252.
Vector analysis, divergence and Stokes' theorem and related integral theorems. Matrix analysis, eigenvalues and eigenvectors, diagonalization. Introduction to ordinary differential equations. Computer software packages for matrix applications, solving, and graphing differential equations.
342B. Methods of Applied Mathematics II (3) I, II
Prerequisite: Mathematics 342A.
Second order ordinary differential equations, power series methods, Bessel functions, Legendre polynomials. Linear partial differential equations, separation of variables, Fourier series, Sturm-Liouville theory, orthogonal expansions, Fourier Transforms. Use of computer software packages for symbolic algebra and solution of differential equations.
350A. Statistical Methods (3) I
Prerequisite: Mathematics 119 or 250 or Biology 215.
One- and two-sample hypothesis tests, paired difference tests, tests for variances, analysis of variance. Linear regression and correlation. Chi-square tests. Simple nonparametric tests. The power of hypothesis tests.
350B. Statistical Methods (3) II
Prerequisite: Mathematics 350A.
Multiple regression, factorial models and nonparametric methods, all with emphasis on applications.
357. Probability and Statistics (3) I, II
Prerequisite: Mathematics 150.
Probability, measures of central tendency and dispersion, characteristics of frequency functions of discrete and continuous variates; applications. Highly recommended for all prospective secondary school teachers of mathematics.
414. Mathematics Curriculum and Instruction (3)
Prerequisites: Senior standing and 12 upper division units in mathematics.
Historical development of mathematics and mathematics curriculum. Principles and procedures of mathematics instruction in secondary schools. For secondary and postsecondary teachers and teacher candidates. Course cannot be used as part of the major or minor in mathematical sciences with exception of major for the single subject teaching credential.
496. Experimental Topics (1-4)
Selected topics. May be repeated with new content. See Class Schedule for specific content. Limit of nine units of any combination of 296, 496, 596 courses applicable to a bachelor's degree.
499. Special Study (1-3) I, II
Prerequisite: Consent of instructor.
Individual study. Maximum credit six units.
NOTE: Proof of completion of prerequisites required for all upper division courses: Copy of transcript.
509. Computers in Teaching Mathematics (3)
Two lectures and three hours of laboratory.
Prerequisite: Mathematics 252.
Solving mathematical tasks using an appropriate computer interface, and problem-based curricula. Intended for those interested in mathematics teaching.
510. Introduction to the Foundations of Geometry (3) I, II
Prerequisite: Mathematics 122 or 151.
The foundations of Euclidean and hyperbolic geometries. Highly recommended for all prospective teachers of high school geometry.
511. Projective Geometry (3)
Prerequisite: Mathematics 254.
Geometry emphasizing relationships between points, lines, and conics. Euclidean geometry and some non-Euclidean geometrics as special cases of projective geometry.
512. Non-Euclidean Geometry (3)
Prerequisite: Mathematics 122 or 151.
History of attempts to prove the fifth postulate; emphasis on plane synthetic hyperbolic geometry; brief treatment of other types of non-Euclidean geometry.
521A. Abstract Algebra (3) I, II
Prerequisites: Mathematics 245 and 252.
Abstract algebra, including elementary number theory, groups, and rings.
521B. Abstract Algebra (3) II
Prerequisite: Mathematics 521A.
Continuation of Mathematics 521A. Rings, ideals, quotient rings, unique factorization, noncommutative rings, fields, quotient fields, and algebraic extensions.
522. Number Theory (3) I
Prerequisites: Mathematics 245 and 252.
Theory of numbers to include congruences, Diophantine equations, and a study of prime numbers.
523. Mathematical Logic (3)
Prerequisite: Mathematics 245.
Propositional logic and predicate calculus. Rules of proof and models. Completeness and the undecidability of arithmetic. Not open to students with credit in Philosophy 521.
524. Linear Algebra (3) I, II
Prerequisites: Mathematics 245 and 254; or 342A.
Vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, normal forms for complex matrices, positive definite matrices and congruence.
525. Algebraic Coding Theory (3) II
Prerequisite: Mathematics 254.
Linear codes, perfect and related codes, cyclic linear codes, BCH codes, burst error-correcting codes.
531. Partial Differential Equations (3) I
Prerequisites: Mathematics 252 and 337.
Boundary value problems for heat and wave equations: eigenfunction expansions, Sturm-Liouville theory and Fourier series. D'Alembert's solution to wave equation; characteristics. Laplace's equation, maximum principles, Bessel functions. Not open to students with credit in Mathematics 340B.
532. Functions of a Complex Variable (3)
Prerequisite: Mathematics 252.
Analytic functions, Cauchy-Riemann equations, theorem of Cauchy, Laurent series, calculus of residues.
533. Vector Calculus (3)
Prerequisite: Mathematics 254 or 342A.
Scalar and vector fields; gradient, divergence, curl, line and surface integrals: Green's, Stokes' and divergence theorems. Green's identities. Applications to potential theory or fluid mechanics or electromagnetism.
534A. Advanced Calculus I (3) I, II, S
Prerequisites: Mathematics 245 and 254; or 342A.
Completeness of the real numbers and its consequences, sequences and series of real numbers, continuity, differentiability and integrability of functions of one real variable.
534B. Advanced Calculus II (3) I, II
Prerequisite: Mathematics 534A.
Series and sequences of functions and their applications, functions of several variables and their continuity, differentiability and integrability properties.
535. Introduction to Topology (3)
Prerequisite: Mathematics 534A.
Topological spaces. Functions, mappings, and homeomorphisms. Connectivity, compactness. Metric spaces.
536. Mathematical Modeling (3) I
Prerequisites: Mathematics 254 and 337 or Mathematics 342A and
342B or Engineering 280.
Advanced models from the physical, natural, and social sciences. Emphasis on classes of models and corresponding mathematical structures. (Formerly numbered Mathematics 636.)
537. Ordinary Differential Equations (3)
Prerequisite: Mathematics 337.
Theory of ordinary differential equations: elementary existence and uniqueness, dependence on initial conditions and parameters, linear systems, stability and asymptotic behavior, plane autonomous systems, series solutions at regular singular points. Not open to students with credit in Mathematics 530.
541. Introduction to Numerical Analysis and
Computing (3) I, II, S
Prerequisites: Mathematics 254 or 342A; and Computer Science
106 or 107 or Engineering 120.
Solution of equations of one variable, direct methods in numerical linear algebra, least squares approximation, interpolation and uniform approximation, quadrature.
542. Introduction to Numerical Solutions of Differential Equations (3) II
Prerequisites: Mathematics 337 and 541.
Initial and boundary value problems for ordinary differential equations. Partial differential equations. Iterative methods, finite difference methods, and the method of lines.
543. Numerical Matrix Analysis (3)
Prerequisite: Mathematics 541.
Gaussian elimination, LU factorizations and pivoting strategies. Direct and iterative methods for linear systems. Iterative methods for diagonalization and eigensystem computation. Tridiagonal, Hessenberg, and Householder matrices. The QR algorithm.
550. Probability (3) I, II, S
Prerequisite: Mathematics 151.
Computation of probability by enumeration of cases, discrete and continuous random variables, density functions, moments, limit theorems, selected distributions. Markov chains, random walks, selected topics.
551A. Mathematical Statistics (3) I, II
Prerequisite: Mathematics 252.
Probability models in the theory of statistics, sampling distributions with applications in statistical inference.
551B. Mathematical Statistics (3) II
Prerequisite: Mathematics 551A.
Point and interval estimation and hypothesis testing in statistical models with applications to problems in various fields.
553. Stochastic Processes (3) II
Prerequisite: Mathematics 550 or 551A.
Introduction to stochastic processes with selected applications.
554A. Computer Oriented Statistical Analysis (3) I
Prerequisite: Mathematics 350A.
Using statistical computer packages such as BMDP and SAS to analyze problems in univariate ANOVA, multiple regression, contingency tables, nonparametric methods and discriminant analysis.
554B. Advanced Computer Oriented Statistical Analysis (3) II
Prerequisite: Mathematics 554A.
Analyze problems in multivariate ANOVA, factor analysis, repeated measures, logistic regression, loglinear models, cluster analysis. Using statistical computer packages.
555. Multivariate Statistical Methods in Biology (3)
(Same course as Biology 597B.)
Two lectures and three hours of laboratory.
Prerequisite: Mathematics 350A.
Application of multivariate statistical methods in the biological sciences.
561. Applied Graph Theory (3)
Prerequisite: Mathematics 245 or 254.
Undirected and directed graphs, trees, Hamiltonian circuits, classical problems of graph theory including applications to linear systems.
562. Mathematical Methods of Operations Research (3) II
Prerequisites: Mathematics 252 and 254.
Theory and applications concerned with optimization of linear and non-linear functions of several variables subject to constraints, including simplex algorithms, duality, applications to game theory, and descent algorithms. Not open to students with credit in Mathematics 362.
579. Combinatorics (3)
Prerequisite: Mathematics 245.
Permutations, combinations, generating functions, recurrence relations, inclusion-exclusion counting. Polya's theory of counting, other topics and applications.
596. Advanced Topics in Mathematics (1-4) I, II
Prerequisite: Consent of instructor.
Selected topics in classical and modern mathematical sciences. May be repeated with the approval of the instructor. See Class Schedule for specific content. Limit of nine units of any combination of 296, 496, 596 courses applicable to a bachelor's degree. Maximum credit of six units of 596 applicable to a bachelor's degree. Maximum combined credit of six units of 596 and 696 applicable to a 30-unit master's degree.
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