This course is designed to introduce early childhood teachers to early mathematics and the Kids Play Math accompanying software. Teachers learn many activities that can be used to integrate early mathematics into the early childhood classroom. Implementation can occur alongside any curriculum to support increased mathematics learning and school readiness. This course is targeted for Head Start teachers in preschool settings.
This course covers number sets, arithmetic operations (using whole numbers, fractions and decimals), working with ratios, proportions and percents, rounding off numbers and using powers and roots of numbers. It extends to algebraic operations, solving elementary equations, the coordinate plane and graphing linear equations. It concludes with elementary logarithms and basic algebraic functions. Hand-held sceintific calculators are used throughout the course. This is a 2-non-degree-credit course. There are no prerequisites.
This course is designed to review the required algebra skills to be successful in MATH 1200. The students study the following topics: review of basic algebra, solving equations and inequalities, rectangular coordinate systems and graphing, polynomial and rational functions, exponential and logarithmic functions, and solving exponential and logarithmic equations.
The seminars offer challenging and interesting mathematical topics that require only high school mathematics. Examples of seminars are Introduction to Crytography, Patterns and Symmetry, Mathematical Art and Patterns of Voting.
This course serves as an introduction to the fundamental concepts in statistics and probability as they apply to the social sciences. The course emphasizes statistical reasoning as it applies to decision-making, the use of probability in thinking about and solving problems, and the interpretation of results. Topics include sampling theory, presenting data using tables, charts and graphs, summarizing and describing data with numerical measures, fundamentals of probability, discrete and continuous probability distributions, the normal probability distribution, sampling distribution, estimation, confidence intervals, hypothesis testing, and regression and correlation. Prerequisite: MATC 1100.
This is a one-quarter course for students in business, social sciences, and liberal arts. It covers elementary differential calculus with emphasis on applications to business and the social sciences. Topics include functions, graphs, limits, continuity, differentiation, and mathematical models. Students are required to attend weekly labs.
Selected topics in algebra and analytic trigonometry intended to prepare students for the calculus sequence (MATH 1951, 1952, 1953). Cannot be used to satisfy the Analytical Inquiry: The Natural & Physical World requirement.
Limits, continuity, differentiation of functions of one variable, applications of the derivative. Students with high school trigonometry should enter th Calculus sequence in fall quarter. Others should complete prerequisite MATH 1750 and enter the Calculus sequence in winter quarter. Prerequisite: MATH 1750 or equivalent.
Differentiation and integration of functions of one variable especially focusing on the theory, techniques and applications of integration. Prerequisite: MATH 1951.
Integration of functions of one variable, infinite sequences and series, polar coordinates, parametric equations. Prerequisite: MATH 1952.
Same topics as MATH 1952 treated rigorously and conceptually. Topics include differentiation and integration of functions of one variable especially focusing on the theory, techniques and applications of integration. Prerequisites: MATH 1951 and permission of instructor.
Same topics as MATH 1953 treated rigorously and conceptually. Topics include integration of functions of one variable, infinite sequences and series, polar coordinates, parametric equations. Prerequisites: MATH 1952 or MATH 1962 and permission of instructor.
Modern propositional logic; symbolization and calculus of predicates, especially predicates of relation. Cross-listed with PHIL 2160.
Matrices, systems of linear equations, vectors, eigenvalues and eigenvectors; idea of a vector space; applications in the physical, social, engineering and life sciences. Prerequisite: MATH 1750 or equivalent.
Solution of linear differential equations; special techniques for nonlinear problems; mathematical modeling of problems from physical and biological sciences. Prerequisite: MATH 1953 or MATH 1963.
Multivariable processes encountered in all sciences; multiple integration, partial differentiation and applications; algebra of vectors in Euclidean three-space; differentiation of scalar and vector functions. Prerequisite: MATH 1953 or MATH 1963.
Introduction to theory of sets; relations and functions; logic, truth tables and propositional calculus; proof techniques; introduction to combinatorial techniques. Prerequisite: high school algebra.
Lectures by alumni and others on surviving culture shock when leaving the University and entering the job world. Open to all students regardless of major. Cross-listed with COMP 3000.
This course surveys major mathematical developments beginning with ancient Egyptians and Greeks and tracing the development through Hindu-Indian mathematics, Arabic mathematics, and European mathematics up to the 18th century. Prerequisite: MATH 1953.
Ordered sets, lattices as relational and as algebraic structures, ideals and filters, complete lattices, distributive and modular lattices, Boolean algebras, duality for finite distributive lattices. Prerequisite: MATH 2200 or MATH 2050.
Zermelo-Fraenkel axioms, axiom of choice, Zorn's Lemma, ordinals, cardinals, cardinal arithmetic. Prerequisite: MATH 2200 or MATH 2050.
Classical propositional calculus (deductive systems and truth-table semantics), first-order logic (axiomatization and completeness), elements of recursion theory, introduction to nonclassical logics. Prerequisite: MATH 2200 or MATH 2050.
Basic probability models, combinatorial methods, random variables, independence, conditional probability, probability laws, applications to classical problems. Prerequisite: MATH 1953.
Limit theorems for independent random variables, multivariate distributions, generating functions. Prerequisites: MATH 2080 and MATH 3080.
Point set topology including topological spaces, connectedness, compactness and separate axioms; preparation for advanced courses in analysis. Prerequisite: MATH 3161 or equivalent.
Vector spaces, linear mappings, matrices, inner product spaces, eigenvalues and eigenvectors. Prerequisite: MATH 2060.
Linear operators on finite dimensional vector spaces, eigenvalues, eigenvectors, Jordan forms; special properties of self-adjoint and normal operators; special topics. Prerequisite: MATH 3151.
A theoretical introduction to the foundations of calculus including sequences, limits, continuity, derivatives and Riemann integration. Prerequisites: MATH 2080 and MATH 2200.
Groups and homomorphisms, isomorphism theorems, symmetric groups and G-sets, the Sylow theorems, normal series, fundamental theorem of finitely generated abelian groups. Prerequisite: MATH 3170.
Examples of groups, permutations, subgroups, cosets, Lagrange theorem, normal subgroups, factor groups, homomorphisms, isomorphisms, rings, integral domains, quaternions, rings of polynomials, Euclid algorithm, ideals, factor rings, maximal ideals, principal ideals, fields, construction of finite fields. Prerequisite: MATH 2200.
Rings, domains, fields; ideals, quotient rings, polynomials; PIDs, UFDs, Euclidean domains; maximal and prime ideals, chain conditions; extensions of fields, splitting fields, algebraic and transcendental extensions; Galois correspondence, the fundamental theorem of Galois theory and applications. Prerequisite: MATH 3170 or equivalent.
Introduction to computability, effective procedures, format languages, undecidability; finite automata and regular languages. Cross-listed with COMP 3221. Prerequisite: MATH 2200 or COMP 2300.
Pushdown automata and context-free languages; Turing machines; decidability, recursive and recursively enumerable sets. Cross-listed with COMP 3222. Prerequisite: MATH 3221 or COMP 3221.
Metric spaces and continuous functions; completeness and compactness; examples including norm spaces; pointwise and uniform convergence; Baire Category Theorem. Prerequisite: MATH 3161 or equivalent.
Linear optimization models, simplex algorithm, sensitivity analysis and duality, network models, dynamic programming, applications to physical, social and management sciences. Prerequisite: MATH 2060.
Nonlinear and stochastic models, elementary queuing theory, integer programming, introduction to simulation; applications to physical, social and management sciences. Prerequisites: MATH 1953 or MATH 1963 and MATH 3311.
Mathematical aspect of options markets, interest rates and discounting; hedging and arbitrage; pricing options with binomial tree models; risk-neutral probabilities and martingales; Brownian motion, geometric Brownian motion and the Black-Scholes formula. Prerequisite: MATH 3080.
Specific geometrical systems including finite, Euclidean, non-Euclidean and projective geometries. Prerequisite: MATH 2200.
Introduction to one-dimensional dynamical systems, fractals; fixed and periodic points; sources and sinks; period doubling and tangent node bifurcations; chaotic dynamical systems; Sarkovskii's Theorem. Prerequisites: MATH 2080 and MATH 2200 and instructor's permission.
Concepts of nonanalytic number theory and its history; prime numbers, divisibility, continued fractions, modular arithmetic, Diophantine equations and unsolved conjectures. Prerequisites: MATH 2200 or MATH 2050.
The principle of inclusion and exclusion, elementary counting techniques, systems of distinct representatives, partitions, recursion and generating functions, Latin squares, designs and projective planes. Prerequisite: MATH 2200.
Varying selected advanced topics in mathematics, depending on student demand and instructor interest.
Paths, cycles, trees, Euler tours and Hamilton cycles, bipartite graphs, matchings, basic connectivity theorems, planar graphs, Kuratowski's theorem, chromatic number, n-color theorems, introduction to Ramsey theory. Prerequisite: MATH 2200 or previous experience with abstract reasoning and basic combinations.
Goals of coding theory and information theory, instantaneous and Huffman codes, Shannon theorems, block and linear codes, generating and parity-check matrices, Hamming codes, perfect codes, binary Golay code, Reed-Muller codes, cyclic codes, BCH codes, Reed-Solomon codes, ideas of convolutional and turbo codes. Prerequisite: MATH 3170.
Complex numbers, analytic functions, complex integration, series expansions, residue theory, conformal maps, advanced topics and applications. Prerequisite: MATH 2080 and MATH 2200.
Advanced topics in complex analysis with applications. Prerequisite: MATH 3851.
Cannot be arranged for any course that appears in regular course schedule for that particular year.
Point set topology including topological spaces, connectedness, compactness and separate axioms; preparation for advanced courses in analysis. Prerequisite: MATH 3161 or equivalent.
Fundamental groups, simplicial homology, Euler characteristic classification of surfaes, manifolds. Prerequisites: MATH 3170 and MATH 3110/4110.
Universal algebras, congruencies, lattices, distributive lattices, modular lattices, Boolean algebras, subdirectly irreducible algebras, Mal'cev theorems, varieties, Birkhoff theorem. Prerequisites: MATH 3170 and either MATH 3040 or MATH 3060.
Groups and homomorphisms, isomorphism theorems, symmetric groups and G-sets, the Sylow theorems, normal series, fundamental theorem of finitely generated abelian groups. Prerequisite: MATH 3170.
Rings, domains, fields; ideals, quotient rings, polynomials; PIDs, UFDs, Euclidean domains; maximal and prime ideals, chain conditions; extensions of fields, splitting fields, algebraic and transcendental extensions; Galois correspondence, the fundamental theorem of Galois theory and applications. Prerequisite: MATH 3170 or equivalent.
Metric spaces and continuous functions; completeness and compactness; examples including norm spaces; pointwise and uniform convergence; Baire Category Theorem. Prerequisite: MATH 3161 or equivalent.
Schwarz and triangle inequalities, Reisz lemma, subspaces and othogonal projections, orthonormal bases, spectrum of bounded linear operators, compact, self-adjoint, normal and unitary operators, spectral theorem and, if time permits, unbounded operators. Also, if time permits, applications to partial differential equations, physics and engineering. Prerequisite: MATH 3260/4260 or MATH 3110/4110.
Definition of Measure spaces; Lebesgue measure; limit theorems; Raydon-Nikodym Theorem; introduction to L=p spaces. Prerequisite: MATH 3260/4260 or MATH 3110/4110.
Topological and measure theoretic dynamical systems; properties and invariants of systems; symbolic dynamics; Ergodic Theorems; applications. Prerequisites: MATH 3120, MATH 4110, MATH 3260, or MATH 4260.
Students research a topic of their choosing with the aid of a faculty member, and then prepare and present a formal lecture on the subject. Prerequisite: graduate standing or consent of the instructor.
Advanced topics in structure of linear spaces; Banach spaces; Hahn-Banach Theorem and Duality; Uniform Boundedness Theorem; Open Mapping and Closed Graph Theorems; Stone-Weierstrass Theorem; Topics in Hilbert Spaces. Prerequisite: MATH 4280.
Basic enumeration techniques; representations of combinatorial objects; algorithms for searching, sorting, generating combinatorial objects, graph algorithms.
varying selected advanced topics in mathematics, depending on student demand. Possible alternatives include of variations, partail differential equations, algebraic topology, differential manifolds, special functions.
Cannot be arranged for any course that appears in course schedule for that particular year.
Research projects undertaken in conjunction with a faculty member.
Techniques, methods used in mathematical, computing research. Includes proofs, bibliographic searching, writing styles, what constitutes an acceptable dissertation.
Cannot be arranged for any course that appears in the regular course schedule for that particular year.
Research leading to a dissertation.