Math 100 is an overview of some of the seminal achievements in mathematics from ancient to modern times. Topics include Problem Solving, Number Theory, Geometry, Fractals, Topology, Probability and Statistics, and applications to other fields.
This course will introduce students to the processes by which valid statistical inferences may be drawn from quantitative data. Topics include design of experiments; sample surveys; measurement; summary and presentation of data; regression and correlation; elementary probability; the law of averages; the central limit theorem; the normal, t and chi-square distributions; confidence intervals; and hypothesis testing. A computer laboratory component will introduce the student to spreadsheets and statistical applications. Offered every semester.
Prerequisite: MATH 104 or sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact score needed). This course, required of biology majors, is a survey of statistical concepts and methods, with an emphasis on concepts critical to the life sciences. Topics include design of experiments; measurement; summary and presentation of data; regression and correlation; elementary probability; the normal, binomial, t-, and chi-square distributions; confidence intervals and standard error; and hypothesis testing. Offered every Spring.
This course is a one semester introduction to statistics with an emphasis on techniques and examples in the social sciences.
This course covers mathematical theory and techniques fundamental to university level scholarship. Topics include: the real number system with number theory concepts (algorithms for computation); percentage; simple and compound interest; linear and exponential functions; systems of linear equations; descriptive statistics. Two hours lecture. Offered every semester.
Prerequisite: MATH 104 or sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact score needed) This course provides the requisite mathematics preparation for Multiple Subject Teaching Credential Candidates. The curriculum satisfies the California Subject Examination for Teachers (CSET) content domain categories: number sense; algebra and functions, measurement and geometry; statistics; data analysis and probability.
Prerequisites: Sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact level needed), or MATH - 104. Applied mathematics and statistics taught through the medium of spreadsheets (Excel). Topics include Introduction to Excel; basic algebra for spreadsheet modeling; descriptive statistics; elementary probability theory.
Prerequisite: MATH 104 or sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact score needed) This course provides a one semester introduction to the theory of differential and integral calculus with an emphasis on technical fundamentals. The curriculum is designed for non-science majors for whom advanced coursework in mathematics is not required.
Prerequisites: Two years of high school algebra and sufficiently high score on the Mathematics placement exam (contact the Mathematics Department for the exact level needed), or MATH - 104. Topics include polynomial functions; factor and remainder theorems; complex roots; exponential, logarithmic, and trigonometric functions; and coordinate geometry. May not be taken for credit after completion of 0206-109. Offered every semester.
Prerequisite: Math 108 or sufficiently high score on the Mathematics placement exam. Differentiation of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions; implicit differentiation; curve sketching; indeterminate forms; velocity and acceleration; optimization; other applications of differentiation; Fundamental Theorem of Calculus, with applications to area and volume. Four hours lecture. Offered every semester.
Prerequisite: MATH - 109. Topics include: Techniques of integration, including trigonometric substitutions, partial fractions, and integration by parts; selected applications of integration, including arc length, surface area, and volume; introduction to differential equations; parametric equations and polar coordinates; infinite sequences and series, including Taylor series. Offered every semester.
Contemporary society is filled with political, economic and cultural issues that arise from mathematical ideas. This service-learning Core mathematics course will engage students in using mathematics as a tool for understanding their world with a focus on the connection between quantitative literacy and social justice.Topics covered will include financial mathematics, voting theory, data representation and statistics.
First Year Seminars are designed and taught by faculty who have a special passion for the topic. All FYSeminars are small classes (16 students) that count toward the university Core. Many FYSeminars include enrichment activities such as excursions into the city or guest speakers. FYSeminars are only open to students in their first or second semester at USF, and students may only take one FYS, in either Fall or Spring. For a detailed description of this course, and other FYSeminars this semester, go to this webpage by cutting and pasting the link: http://www.usfca.edu/artsci/firstyearsem/
Prerequisite: CS 110 and Math 108, or permission of instructor. Topics include algebraic structures, graph theory, combinatorics, and symbolic logic. Offered every Fall.
Matrix arithmetric and matrix algebra (determinants, adding and multiplying matrices, matrix inverse, using matrices to solve systems of equations), geometric applications of linear algebra (matrices as transformations, vectors in 2- and 3-dimensions, equations of planes, etc.); discrete probability, random variables, discrete and continuous probability distributions (including binomial and normal), expected value and variance. Offered every Spring.
Prerequisite: MATH - 110. Topics include analytic geometry in three dimensions; vector functions; arc length and curvature; motion in space; partial differentiation and chain rule; directional derivative and gradient; optimization and Lagrange multipliers; multiple integrals, line integrals, and surface integrals; divergence and curl; theorems of Green, Gauss, and Stokes. Offered every Fall.
Prerequisites: MATH - 109. Topics include systems of linear equations, matrices and determinants; the geometry of vectors in Euclidean space; general properties of vector spaces, bases and dimension; linear transformations in two and three dimensions, eigenvalues and eigenvectors. Offered every Fall.
Prerequisite: MATH - 110. Topics include logic and mathematical proof; set theory, equivalence relations, and mappings; mathematical induction; modular arithmetic; isomorphism; groups; structures of real numbers; convergence and continuity. Emphasis on concepts of proof and mathematical formalism. Offered every Spring.
Students-In-Transition (SIT) Seminars are designed and taught by faculty who have a special passion for the topic. All SIT Seminars are small classes (16 students) that count toward the university Core. Many SIT Seminars include enrichment activities such as excursions into the city or guest speakers. SIT Seminars are only open to transfer students who are in their first or second semester at USF, and students may only take one SIT Seminar, in either Fall or Spring. For a detailed description of this course, and other SIT Seminars this semester, go to this webpage by cutting and pasting the link: http://www.usfca.edu/artsci/firstyearsem/
Prerequisite: MATH - 110 or permission of instructor. An informal, discussion-oriented class to develop skills for investigating and solving mathematical problems. Topics include elementary mathematics, combinatorics, geometry, number theory and calculus, as well as problems from contests such as the International Mathematical Olympiad and the Putnam Examination. Strongly recommended for students interested in teaching mathematics.
Prerequisite: MATH - 110 or permission of instructor. A history of the development of arithmetic, algebra, geometry, and calculus. Selected topics from recent mathematical history.
An introduction to the Eastern European Mathematical Circles culture. Students will learn mathematical folklore and problem-solving methods drawn from geometry and discrete mathematics, and will both observe and teach students in several mathematical circles in the Bay Area. In addition to the mathematics and pedagogy, students will explore issues of equity in educational opportunity. This is a service earning course designed for math, physics, or computer science majors who are interested in teaching.
Prerequisites: MATH - 130 or PHYS - 110 , and MATH - 211 , or permission of instructor. Topics include a review of first-and second-order equations, series solutions, systems of linear and non-linear differential equations, numerical methods, qualitative methods, introduction to partial differential equations.
Prerequisites: MATH - 110 and MATH - 130. The methodology of mathematical modeling will be explored in several case studies from fields as diverse as political science, biology, and operations research. Problems of data collection, model fitting, and model analysis will be explored. Case studies incorporate topics from: analysis of conflict (business, military, social), population dynamics, and production management.
This is one semester colloquium course. Students will be exposed to approximately 7 talks over the course of the semester on various topics of interest in modern mathematics. This course is intended for mathematics majors and minors. A student can take up to 2 units of colloquium for credit, but the unit cannot be applied to count for required classes.
Prerequisites: MATH 230 and MATH 211, or permission of instructor. Topics include integration and differentiation of functions of a complex variable, Laurent series, conformal mapping, residues, and Cauchy's theorems.
Prerequisite: MATH - 235 or permission of instructor. Topics include prime numbers, congruences, quadratic reciprocity, number-theoretic functions, and diophantine equations.
Pre-requisite: MATH 110 OR permission of instructor. Topics may include discrete and continuous random variables, probability distributions functions; mathematical expectation; joint density functions, law of large numbers; central limit theorem, probability models and applications, stochastic processes, Markov processes.
Prerequisite: Math 370, or permission of instructor. This course introduces students to theoretical issues and data-driven applications in statistics. Topics include descriptive statistics and data analysis; confidence intervals and hypothesis tests; estimation theory, linear regression, goodness-of-fit tests, and nonparametric tests.
Prerequisite: MATH - 110 or permission of instructor. Topics chosen from axiomatics, Euclidean and non-Euclidean geometries, vector spaces and inner products, and symmetry groups.
Prerequisite: Permission of instructor. This course offers selected upper division students an opportunity to work on a sponsored research project under the direction of a faculty member. May be repeated for credit. Offered as often as suitable projects can be found.
Prerequisite: Permission of instructor. This course treats topics not covered in other Mathematics courses, but of interest to faculty and students. May be repeated for credit. Offered intermittently.
Prerequisite: Written consent of instructor and dean. May be repeated for credit. Offered every semester.
Prerequisite: MATH - 235 or permission of instructor.. An in-depth study of combinations and permutations, inclusion-exclusion, the binomial theorem, recurrence relations, and graph theory, with additional topics depending on student and instructor interest (for example, generating functions, combinatorial number theory, finite-state machines). Offered every other Fall.
Prerequisite: MATH - 235 or permission of instructor. Topics include an introduction to the theory of groups, rings, fields, vector spaces, and other algebraic structures.
Prerequisites: MATH 211 and MATH 235 or permission of instructor. Topics include sequences and series, topology of the real line, limits and continuity, the real number system, the derivative and Riemann integral.
Prerequisite: MATH - 211 or permission of instructor. Topics include classical differential geometry of curves and surfaces, curvature, the bending of surfaces, shortest paths in a surface, and tensors in geometry and physics.
Prerequisite: MATH 235 or permission of instructor Topics selected from point-set topology, algebraic topology, geometric topology, and differential topology.
Prerequisites: CS 112 (grade of C or better) and MATH 202 (grade of C or better). Floating point representation of numbers, error analysis, root finding, interpolation, numerical integration and differentiation, numerical solution of linear systems, numerical solution of differential equations. Four hours lecture.