Mathematics Course Offerings

BASIC SKILLS COURSES

• MATH 0801, 0802 Elementary Algebra A and B (4 each)

  A two-quarter sequence in basic mathematics and elementary algebra. CR/NC grading only. On successful completion of this sequence, students should register for MATH 0950. Units will not count toward the baccalaureat degree.
  Prerequisite: Appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm).
  

  
  

• MATH 0900 Elementary Algebra (4)

  A one quarter course in elementary algebra. CR/NC grading only. On successful completion of this course, students should register for MATH 0950. Not open to students who have passed MATH 0802. Units will not count toward the baccalaureate degree.
  Prerequisite: Appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm).
  

  
  

• MATH 0950 Intermediate Algebra (4)

  Operations with algebraic expressions, exponents and radicals; linear and quadratic equations; systems of equations and inequalities; linear and quadratic functions and their graphs; elementary conic sections; word problems. CR/NC grading only. Units will not count toward baccalaureate degree.
  Prerequisite: Grade of CR in 0802 or MATH 0900 or an appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm).
  

UNDERGRADUATE COURSEWORK

• MATH 1110 The Nature of Mathematics (4) [CAN MATH 2]

  This course is designed to introduce the student to mathematics as an art and mathematics as a tool, emphasizing the place of mathematics in today's world. Will satisfy the general education education requirement for nonmajors.
  Prerequisites: Satisfactory completion of Entry Level Mathematics requirement.
  

  
  

• MATH 1130 College Algebra (4)

  Functions and graphs: polynomials, rational functions, exponential and logarithmic functions.
  Prerequisites: Satisfactory completion of Entry Level Mathematics requirement.
  

  
  

• MATH 1300 Trigonometry and Analytic Geometry (4)

  Definitions, properties and graphs of the trigonometric functions. Applications. Analytic geometry of conic sections. A preparatory course for calculus.
  Prerequisites: MATH 1130 or departmental permission
  

  
  

• MATH 1304 Calculus I (4)

  Differential calculus. Limits and continuity. Exponential and logarithmic functions. Techniques and applications of differentiation.
  Prerequisite: MATH 1300 or departmental permission
  

  
  

• MATH 1305 Calculus II (4)

  Integral calculus. The indefinite integral, area, the Fundemental Theorem and techniques of integration. Applications of volume, arc length, physical and biological problems.
  Prerequisite: MATH 1304 or departmental permission
  

  
  

• MATH 1810 Mathematics for Business and Social Sciences I (4)

  Precalculus review, limits and continuity, differential calculus including derivatives of polynomial, exponential and logarithmic functions, integral calculus, applications to business and social sciences.
  Prerequisites: MATH 1130 or satisfactory score on placement test. Not open for students who have received credit for MATH 1803
  

  
  

• MATH 1820 Mathematics for Business and Social Sciences II (4)

  Multivariable calculus, Lagrange multipliers, elementary differential equations, systems of linear equations, matricies, determinants, difference equations, elementary graph theory, applications to business and social sciences.
  Prerequisites: MATH 1810. Not open for students who have received credit for MATH 1802
  

  
  

• MATH 2011 Number Systems (4)

  Structure of number systems, place value, whole numbers, integers, fractions, decimals, real numbers. Standard and nonstandard algorithms, mental computation. Algebra as generalized arithmetic. Divisibility, prime and composite numbers, GCF, LCM. Ratio, proportion, percents. Not open to students with credit for MATH 4021.
  Prerequisite: satisfactory completion of the Entry Level Mathematics (ELM) requirement.
  

  
  

• MATH 2101 Elements of Linear Algebra (4)

  Vector spaces, linear transformations, matrices, systems of linear equations. Stress on 2 and 3 dimensions, including geometric and other applications.
  Prerequisite: MATH 1305 or 1820 (may be taken simultaneously with, or after, MATH 2304)
  

  
  

• MATH 2150 Discrete Structures (4)

  Topics in discrete mathematics. Elementary logic, set theory, and relations; induction, enumeration techniques, recurrence relations, trees and graphs. Boolean algebra, algorithm analysis.
  Prerequisite: MATH 1304
  

  
  

• MATH 2304 Calculus III (4)

  Infinite series, convergence of power series. Vectors in space. Partial derivatives, chain rule, directional derivative and gradient. Curves and surfaces. Maxima and minima. Multiple integrals.
  Prerequisite: MATH 1305
  

  
  

• MATH 3000 Introduction to Abstract Mathematics and Proofs (4)

  Introduction to methods and proof techniques in several branches of mathematics, with topics chosen from logic, set theory, abstract algebra, number theory, analysis, and graph theory. Provides a transition from lower division mathematics courses, which concentrate on computation, to upper division proof-oriented mathematics courses. Mathematics majors may substitute this course for MATH 2150.
  Prerequisite: MATH 2304; co-requisite: MATH 2101
  

  
  

• MATH 3100 Linear Algebra (4)

  Abstract vector spaces, linear transformations, matrices and determinants. Dual spaces and inner product spaces. Eigenvalues and eigenvectors.
  Prerequisites: MATH 2101 and either 2150 or 3000
  

  
  

• MATH 3121 Abstract Algebra I (4)

  Equivalence relations, binary operations. Integers: divisibility, factorization, integers modulo n. Groups: subgroups, cyclic groups, permutation groups, quotient groups. Homomorphisms and isomorphisms. Selected topics as time permits.
  Prerequisites: MATH 2101 and either 2150 or 3000
  

  
  

• MATH 3122 Abstract Algebra II (4)

  Rings and fields: integral domains, ideals, quotient rings polynomial rings, roots of polynomials, algebraic extensions and finite fields. Selected topics as time permits.
  Prerequisite: MATH 3121
  

  
  

• MATH 3151 Combinatorics (4)

  Theory of counting, including partitions, Stirling numbers, generating functions. Applications of Burnside's Lemma from multiple transitivity to the Polya- Redfield Theorem. Ferrers diagrams, symmetric functions, and majorization.
  Prerequisites: MATH 2101 and either 2150 or 3000
  

  
  

• MATH 3215 Geometry I (4)

  An axiomatic approach to incidence, Neural, Euclidean, and non-Euclidean plane geometry. Various models, such as the Euclidean, hyperbolic, taxicab planes, will be considered throughout the course.
  Prerequisites: MATH 2101 and either 2150 or 3000
  

  
  

• MATH 3300 Analysis I (4)

  The real numbers, limits, sequences and series of real numbers, Bolzano-Weierstrass theorem. Continuity, intermediate and extreme value theorems, uniform continuity, sequences of functions. Topology of Rⁿ. Differentiation, chain rule, implicit and inverse function theorems.
  Prerequisites: MATH 2101, 2304 and either 2150 or 3000
  

  
  

• MATH 3301 Analysis II (4)

  The real numbers, limits, sequences and series of real numbers, Bolzano-Weierstrass theorem. Continuity, intermediate and extreme value theorems, uniform continuity, sequences of functions. Topology of Rⁿ. Differentiation, chain rule, implicit and inverse function theorems.
  Prerequisite: MATH 3300
  

  
  

• MATH 3320 Calculus of Vector Functions(4)

  Differentiation and integration of vector valued functions; gradient, divergence, and curl; cylindrical and spherical coordinates; theorems of Green and Stokes.
  Prerequisites: MATH 2304 and MATH 2101 (2101 may be taken concurrently)
  

  
  

• MATH 3331 Differential Equations(4)

  Methods of solution and applications of first order differential equations. Linear n-th order equations with emphasis on equations of 2nd order. Other topics may include power series solutions, Laplace transforms, linear systems.
  Prerequisite: MATH 2304
  

  
  

• MATH 3361 Ordinary Differential Equations(4)

  Series solution of linear differential equations with variable coefficients, two point boundary value problems, systems of differential equations, phase plane analysis
  Prerequisites: MATH 2101 and MATH 3331
  

  
  

• MATH 3401 Introduction to Probability Theory I (4)

  The theory of probability with applications to science and engineering. Sample spaces; random variables; joint, marginal, conditional distributions; expectations; important distributions (binomial, Poisson, normal, etc.); and moment generating functions.
  Prerequisite or concurrent: MATH 1305
  CROSS-LISTED: STAT 3401
  

  
  

• MATH 3402 Introduction to Probability Theory II (4)

  Generating functions and multivariate distributions. Conditioning. Chebyshev inequality and limit theorems. Multidimensional transformations of random variables. Derivation of t and F distributions. Uses of probability theory in mathematical statistics.
  Prerequisites: MATH 2304 or concurrent, MATH/STAT 3401
  CROSS-LISTED: STAT 3402
  

  
  

• MATH 3502 Statistical Inference I (4)

  Random variables, sampling distributions (binomial, Poisson, normal, exponential), conditional probability. Estimation, hypothesis testing. Computer-aided computations. Topics include: t-tests; correlation, regression; proportions, chi-squared; ANOVA.
  Prerequisites: MATH 1305 or MATH 1820
  CROSS-LISTED: STAT 3502
  

  
  

• MATH 3503 Statistical Inference II (4)

  General linear hypothesis with emphasis on design and analysis of experiments. Data from science, engineering, and quality management. Factorial designs: random effects, nesting. Optional topics: incomplete blocks, missing data, analysis of covariance. Computer-aided analysis.
  Prerequisites: MATH/STAT 3502
  CROSS-LISTED: STAT 3503
  

  
  

• MATH 3600 Number Theory (4)

  Euclid's algorithm, prime numbers, congruences, theorems of Fermat and Euler, quadratic residues.
  Prerequisites: MATH 2101 and either 2150 or 3000
  

  
  

• STAT 3601 Introductory Statistics and Probability for Science and Engineering (4)

  Basic probability rules (independence, Bayes' Theorem), distributions (binomial, Poisson, normal, exponential), reliability. Descriptive, inferential statistics (control charts, estimation, hypothesis testing: one, two samples), correlation, regression. Emphasizes: computer analysis, simulation; science, engineering applications.
  Prerequisite: MATH 1305 CROSS-LISTED: ENGR 3601
  

  
  

• MATH 3750 Numerical Analysis I (4)

  Basic numerical methods and analysis; practical solutions of problems from engineering, science, and mathematics. Computer representation of real numbers, errors, root finding, interpolation, numerical integration, ordinary differential equations.
  Prerequisites: CS 1160, MATH 2101 and 2304
  

  
  

• MATH 3841 Linear Programming (4)

  Problems of maximizing or minimizing a linear function subject to linear constraints; typical applications involve planning ("programming") the allocation of limited resources to achieve an optimal result. Topics include problem formulation, solution procedures, duality theory, sensitivity analysis, special problems ( e.g., transportation and assignment problems).
  Prerequisites: MATH 2304 and competence in matrix algebra
  CROSS-LISTED: ENGR 3841
  

  
  

• MATH 3865 Mathematical Modeling (4)

  Discrete and continuous mathematical models. General introduction to the use of difference and differential equations, probability and statistics, and matrices for solving realistic problems. Computer simulation. Emphasis on effective written reports.
  Prerequisites: MATH 2101 and MATH 2304
  CROSS-LISTED: STAT 3865
  

  
  

• MATH 3875 Mathematical Physics (4)

  Mathematics theory and methods with applications to physics. In class physics laboratory explorations will utilize mathematical techniques to better understand physics phenomena.
  Prerequisite: MATH 1305, Co-requisite: MATH 2304
  

  
  

• MATH 3898 Cooperative Education (4)

  Supervised work experience in which student completes academic assignments integrated with off-campus paid or volunteer activities. May be repeated for up to 8 units. A maximum of 2 units will be accepted toward the Mathematics major. CR/NC grading only.
  Prerequisites: at least 2.0 GPA; departmental approval of activity; completion of lower-division Mathematics major requirements and upper division standing.
  

  
  

• MATH 4012 Geometry and Measurement (4)

  Properties of 2- and 3-dimensional figures including congruence, similarity, proportional reasoning, area, perimeter, volume, surface area. Informal constructive proofs of properties of angles, polygons, parallel lines and Pythagorean theorem. Transformational geometry. Measurement systems, estimation, coordinate geometry. Not open to students with credit for MATH 4022.
  Prerequisite: MATH 2011
  

  
  

• MATH 4013 Statistics, Data Analysis, and Probability (4)

  Displaying and interpreting data via graphs, tables and charts. Descriptive statistics, including mean, median, mode and range. Basic Survey design, including possible sources of biases. Elementary discrete probability. Dependent and independent events. Cross-listed with STAT 4013. Not open to students with credit for MATH 4023.
  Prerequisites: MATH 2011 and satisfactory completion of the Entry Level Mathematics requirement.
  

  
  

• MATH 4014 Algebra and Function (4)

  Patterns and functional relationships. Linear and quadratic equations and inequalities. Interpretation of graphs, multiple representations of functions. Factoring and completing the square. Proportional reasoning. Systems of linear equations. Not open to students with credit for MATH 4024.
  Prerequisites: MATH 2011 and satisfactory completion of the Entry Level Mathematics requirement.
  

  
  

• MATH 4040 History of Mathematics (4)

  The historical development of mathematical ideas and techniques.
  Prerequisite: Calculus or the consent of instructor
  

  
  

• MATH 4105 Multilinear Algebra (4)

  Introduction to partitions of positive integers; inner product spaces, including such topics as unitary, hermitian, normal matrices; certain ``combinatorial'' properties of permutation groups. Applications to matrix representations of finite groups and topics in tensor spaces.
  Prerequisites: MATH 3100 and MATH 3121
  

  
  

• MATH 4121 Advanced Algebra (4)

  Theory of groups, including factor groups, Jordan-Holder Theorem, Sylow theorems. Mappings and homomorphisms. Introduction to rings and fields. Topics continued in MATH 6121.
  Prerequisite: MATH 3122
  

  
  

• MATH 4151 Graph Theory (4)

  Introduction to graph theory. Graphic sequences. Planar graphs and the theorems of Euler and Kuratowski. Bipartite graphs. Connectivity and spanning trees. Hamiltonian graphs. Matching, chromatic and characteristic polynomials. Cospectral graphs and the graph isomorphism problem. Algorithms.
  Prerequisites: MATH 2101 and either 2150 or 3000
  

  
  

• MATH 4170 Theory of Automata (4)

  Formal models of automata, language, and computability and their relationships. Finite automata and regular languages. Push-down automata and context-free languages. Turing machines, recursive functions, algorithms and decidability.
  Prerequisites: MATH 2101, MATH 2150, MATH 2304
  CROSS-LISTED: CS 4170
  

  
  

• MATH 4215 Topics in Geometry (4)

  Topics in geometry such as algebraic, differential, finite, or projective geometry, convexity, packing and tiling, polytopes, and isoperimetric problems.
  Prerequisites: MATH 3215 or consent of instructor. May be repeated once for credit with consent of the chair.
  

  
  

• MATH 4235 Introduction to Knot Theory (4)

  An introduction to the theory of knots and links. Reidemeister moves, knot invariants, including 3-colorings, linking number, Alexander polynomial, Kauffman bracket and Jones polynomial. As time permits some applications in biology and/or chemistry will be discussed. Prerequisite: MATH 3121
  

  
  

• MATH 4245 Analysis of Algorithms (4)

  Design, analysis and implementation of algorithms. Methods of algorithm design, including recursion, divide and conquer, dynamic programming, backtracking. Time and space complexity analyses in the best, worst, average cases. NP-completeness; computationally hard problems. Applications from several areas of Computer Science.
  Prerequisites: MATH 2101, MATH 2304, CS 3240
  CROSS-LISTED: CS 4245
  

  
  

• MATH 4250 Differential Geometry and Topology (4)

  Introduction to modern differential geometry and topology. Geometry of curves and surfaces, differential forms and vector fields, manifolds, curvature, geodesics, topological invariants.
  Prerequisites: MATH 3100, 3300, or consent of instructor
  

  
  

• MATH 4301 Analysis III (4)

  Manifolds and smooth maps, vector fields and differential forms, Riemann integration for functions of several variables, Fubini theorem, theorem of Green, Gauss, and Stokes, general Stokes theorem.
  Prerequisite: MATH 3301
  

  
  

• MATH 4340 Introduction to Complex Variables (4)

  Introduction to theory of functions of complex variables.
  Prerequisites: MATH 3300
  

  
  

• MATH 4350 Theory of Functions of a Real Variable (4)

  Pointwise and uniform convergence, Taylor series, Riemann integration, sets of measure zero, Lebesgue's theorem on the Riemann integral, the metric space of continuous functions, and selected topics.
  Prerequisite: MATH 3300
  

  
  

• MATH 4360 Introduction to Topology (4)

  Topological spaces, metric spaces, continuity, connectedness and compactness.
  Prerequisites: MATH 3300
  

  
  

• MATH 4361 Partial Differential Equations (4)

  Differential equations of physics: the wave equation, the heat equation, Laplace's equation; boundary-value problems. Elementary Sturm-Liouville theory. Fourier series, Fourier and Laplace transforms, Bessel functions, selected topics.
  Prerequisite: MATH 3331
  

  
  

• MATH 4365 Dynamical Systems (4)

  Introduction to dynamical systems and applications. Variational calculus, Lagrangian dynamics, principle of critical action, Hamiltonian system and symplectic mechanics, Hamilton-Jacobi equation, chaotic and nonlinear systems, fractals.
  Prerequisites: MATH 3100, 3300, 3331, or consent of instructor
  

  
  

• MATH 4380 Geometry and Topology of Dynamical Systems (4)

  Introduction to geometrical and topological aspects of dynamical systems. Manifolds, bundles, vector fields, and differential forms. Lagrangian and Hamiltonian systems and symplectic mechanics.
  Prerequisites: MATH 3100 and MATH 3300, or consent of instructor
  

  
  

• MATH 4401 Introduction to Stochastic Processes (4)

  Markov chains, birth-death processes, queueing models, limit theorems. Computer simulation. Science, engineering applications include inventory models, reliability, epidemiology, dynamic programming.
  Prerequisite: MATH 2304 (or concurrent) and either MATH/STAT 3401 or 3502
  CROSS-LISTED: ENGR 4401 and STAT 4401
  

  
  

• MATH 4750 Numerical Analysis II (4)

  Continuation of MATH 3750. Numerical solution of linear systems, matrix norms, approximation of functions, algebraic eigenvalues.
  Prerequisite: MATH/CS 3750
  CROSS-LISTED: CS 4750
  

  
  

• MATH 4841 Topics in Optimization (4)

  Sequel to MATH 3841. Topics to be drawn from linear and/or nonlinear programming. Linear programming topics may include integer programming, game theory, network programming; nonlinear programming topics include optimality conditions and solution procedures for unconstrained and constrained optimization problems. May be repeated once for credit with consent of the chair.
  Prerequisite: MATH 3841
  

  
  

• MATH 4850 Variational Calculus (4)

  Function spaces, general variation of a functional, Euler-Lagrange equations, Noether's theorem and conservation laws, Hamilton-Jacobi theory, canonical transformations and symplectic geometry.
  Prerequisite: MATH 3100 and MATH 3331
  

  
  

• MATH 4900 Independent Study (1-5)

  
  Prerequisites: Permission from Instructor and Dept Chair
  

  
  

• MATH 4901 Senior Seminar (4)

  Exploration of topics in mathematics. Topics selected from the literature to illustrate relationships among various areas of mathematics. Oral presentations and paper required.
  Prerequisite: senior standing in mathematics (completion of 32 units of mathematics courses) or permission of the instructor.
  

Graduate Coursework