U20 Math 1011 Introduction to Statistics

This course covers basic concepts of statistics, including data collection (sampling and designing experiments), data organization (tables, graphs, frequency distributions, numerical summarization of data), and statistical inference (elementary probability and hypothesis testing). Prerequisite: High school algebra. This course is not equivalent to L24 1011.

Credit 3 units. UColl: OLI

U20 Math 133 Programming with Python

An introductory course for students with little or no programming experience. Topics include the software development process, documentation, debugging, and testing within the commonly used Python environment. At the end of the course students should be able to write and debug basic programs to display and interpret data using accepted programming conventions and styles.

Credit 3 units. UColl: OLI

U20 Math 140 Algebra

This College Algebra with Integrated Review Course is designed to support students who have not taken a math class recently. This course's applications will focus on STEM related fields such as biology, chemistry, and pre-med. Topics covered in this course include: basic rules of operation in the real number system, sets, equations and graphing, inequalities, relations and functions, systems of equations, exponential and log equations, and rational zeros of polynomials. Prerequisite: one year of high school algebra or equivalent.

Credit 3 units. UColl: OLI

U20 Math 141 Topics in Precalculus

A study of the properties of algebraic and trigonometric functions in preparation for further coursework in calculus. Topics covered include the continuation of the study of polynomial, exponential and logarithmic functions and a foundation in trigonometry, including analytic trigonometry and application and polar coordinates. U20-140 and 141 serve as preparation for the calculus sequence. Prerequisite: high school or college algebra.

Credit 3 units.

U20 Math 155 Calculus I

First course in differential calculus covering functions, limits, continuity, derivatives, techniques of differentiation, and applications including maxima and minima of functions, curve sketching, related rates and rectilinear motion, mean value theorem. Prerequisite: U20-141 or equivalent, including trigonometry.

Credit 3 units. UColl: OLH, OLI

U20 Math 156 Calculus II

Continuation of U20 155, starting with a brief review of definitions and formulas. The concept of the integral; the Fundamental Theorem of Calculus; techniques of integration; application of the integral including areas, volume, and work; differential and integral calculus with elementary transcendental functions. Prerequisite: U20 155 or equivalent.

Credit 3 units. UColl: OLI

U20 Math 205 Applied Statistics

This is a first course in statistics, with examples and applications from a variety of disciplines and emphasis on the social, behavioral, and natural sciences. Students learn about key topics and statistical methods that may be applied to areas such as economics, mathematics, psychology, business, and health sciences, to name a few. The course provides a foundation in descriptive and inferential statistics as well as in probability. Students learn numerical and graphical methods of describing data and study some of the more common distributions. Topics include hypothesis testing, confidence-interval estimation, correlation, regression, analysis of variance, contingency tables, quality control, and nonparametric statistics. This course may be applied to University College majors in economics, managerial economics, mathematics, and political science. This course is entirely web-based, with all course components online. U20 Math 205 and U20 Math 305 may not both be taken for credit. Prerequisite: College algebra.

Credit 3 units. UColl: OLI

U20 Math 210 The Art of Mathematical Thinking

Mathematics plays an important role in society, from engineering to architecture to the social and behavioral sciences. This course will expose non-math majors to fascinating sides of mathematics that are typically not discussed in standard math courses. Students will learn effective thinking techniques with applications beyond standard mathematics, and discover exciting ideas and new perspectives about the world. We will look at questions like: What do rabbits, piano keyboards, and pine cones have to do with the Parthenon? What do secret codes and bar codes have to do with number systems and prime numbers? What are some uses and misuses of mathematics in everyday life? Why are coincidences not so amazing after all? Prerequisite: proficiency in high school algebra.

Credit 3 units. UColl: OLI

U20 Math 224 Advanced Data Visualization (with R)

Visual representations of data are important for conveying complex information simply. There are many packages available in R (e.g., ggplot2) that can be used to generate plots and graphs of various kinds. Sometimes the default output from a particular command is not the best way to communicate a particular result or trend. This course will help students to learn more about the common ways to display data as well as how to make changes to the codes so that the visualizations are more effective. Visualization techniques involve study from areas such as graphic design, computer science, psychology, and mathematics. Topics covered will include categorical data, distributions, time series, scatter plots, and maps. Prerequisites: Math 124 and Math 205 or Math 305 or equivalents.

Credit 3 units. UColl: OLH, OLI

U20 Math 230 Introduction to Data Science with Python

In this continuation of Programming with Python, students apply their skills to data science examples. The course will start with a brief review of Python and then shift to technical topics such as working with the numerical library NumPy; data manipulation with pandas; and creating graphics with matplotlib, Seaborn and other data visualization libraries. The final project will be an application of machine learning using the scikit-learn library. Prerequisite: U20 133 or permission of the instructor.

Credit 3 units. UColl: NSC, OLI

U20 Math 255 Calculus III

Continuation of U20 156. Vectors in the plane and in space, lines and planes in space, calculus of vector-valued functions, parametric equations, arc length, polar coordinates, infinite series, Taylor's theorem. Prerequisite: U20 156 or equivalent.

Credit 3 units. UColl: OLI

U20 Math 256 Calculus IV

Continuation of U20 255. Functions of several variables, partial derivatives, tangent planes, directional derivatives, total differential, multiple integrals, line integrals, and an introduction to elementary differential equations. Prerequisite: U20 255 or equivalent.

Credit 3 units. UColl: OLI

U20 Math 3001 Independent Study in Mathematics

Credit 3 units.

U20 Math 301 Differential Equations

First course in differential equations with emphasis on linear equations and their applications. Prerequisite: U20 256 or equivalent.

Credit 3 units.

U20 Math 305 Probability and Statistics

Discrete and continuous random variables, mean and variance, hypothesis testing and confidence limits, nonparametric methods. Students' t-methods, regression, correlation. Prerequisite: U20 156 or consent of department.

Credit 3 units.

U20 Math 309 Linear Algebra I

Detailed treatment of the algebra of matrices. Rank and equivalence of matrices. Matrices over a number field. Linear equations and linear dependence. Determinants. Prerequisite: U20 256 or equivalent.

Credit 3 units. UColl: OLI

U20 Math 3091 Matrix Algebra

An introductory course in linear algebra that focuses on Euclidean n-space, matrices and related computations. Topics include: systems of linear equations, row reduction, matrix operations, determinants, linear independence, dimension, rank, change of basis, diagonalization, eigenvalues, eigenvectors, orthogonality, symmetric matrices, least square approximation, quadratic forms. Introduction to abstract vector spaces. Prerequisite: Math 132.

Credit 3 units. Arch: NSM Art: NSM

U20 Math 3101 Foundations for Higher Mathematics

This course provides an introduction to the rigorous techniques used in more advanced mathematics. Topics include propositional logic, the use of quantifiers, set theory, methods of proof and disproof (counterexamples), and foundations of mathematics. The use of these tools in the construction of number systems and in other areas such as elementary number theory, combinatorial arguments, and elementary proofs in analysis is also covered. Prerequisite: Math 233.

Credit 3 units. Arch: NSM Art: NSM

U20 Math 400 Independent Study

Credit variable, maximum 3 units.

U20 Math 420 Experimental Design

A first course in the design and analysis of experiments, from the point of view of regression. Factorial, randomized block, split-plot, Latin square, and similar design. Prerequisite: CSE 131 or 200, Math 3200, or permission of instructor.
Same as U20 Math 520

Credit 3 units. Art: NSM

U20 Math 493 Probability

Mathematical theory and application of probability at the advanced undergraduate level; a calculus-based introduction to probability theory. Topics include the computational basics of probability theory, combinatorial methods, conditional probability including Bayes' theorem, random variables and distributions, expectations and moments, the classical distributions, and the central limit theorem.
Same as U20 Math 593

Credit 3 units.

U20 Math 494 Mathematical Statistics

Theory of estimation, minimum variance and unbiased estimators, maximum likelihood theory, Bayesian estimation, prior and posterior distributions, confidence intervals for general estimators, standard estimators and distributions such as the Student-t and F-distribution from a more advanced viewpoint, hypothesis testing, the Neymann-Pearson Lemma (about best possible tests), linear models, and other topics as time permits. Prereq: Math 305 and U20 593, or permission of the instructor.
Same as U20 Math 594

Credit 3 units. UColl: OLI