# Mathematics (MTH)

**MTH 201 Principles of Mathematics 3 Units**

Through a study of mathematics competencies required for the liberal studies major, this course will include logic, algebra, functions, counting, probability, and statistics with problem solving being emphasized throughout the course. Prerequisite: Intermediate Algebra or equivalent.

**MTH 252 Introduction to Calculus 3 Units**

This course, for non-math majors, will study the limits and the foundations of differential and integral calculus with an emphasis on applications. The use of technology (graphing calculator, websites, Maple) will be used. Prerequisite: C- or better in AMTH 101 or CMTH 101 or MTH 201 or equivalent.

**MTH 265 Introduction to Statistics 3 Units**

As a basic statistics course applicable to education, business, and the hard sciences, this course will include topics such as descriptive statistics, the normal, binomial, F-, and Chi-squared distributions, and hypothesis testing. Optional topics might include additional non-parametric tests and ANOVA. A TI-83 graphing calculator or Microsoft Excel is required. Prerequisite: C- or better in AMTH 101 or CMTH 101 or MTH 201 or MTH 252 or MTH 271 or equivalent.

**MTH 271 Calculus I 4 Units**

This course will study differential and integral calculus in one variable through graphical, numerical and symbolic methods. Limits, continuity, derivatives, and integrals will be studied with algebraic, trigonometric, exponential and logarithmic functions, including applications using calculus to solve problems. Prerequisite: A passing score on the Calculus Placement Exam, or consent of the department chair.

**MTH 272 Calculus II 4 Units**

A continuation of MTH 271, this course will include a study of methods of integration, applied to algebraic and transcendental functions. Solids of revolution, definite and indefinite integrals, Taylor polynomials, sequences and series, will be studied including applications using calculus to solve problems. Prerequisite: C- or better in MTH 271 or acceptable AP examination credit.

**MTH 301 Mathematics for Teachers 3 Units**

This course is designed to meet the California Commission on Teacher Credentialing (CCTC) criteria for students studying to become elementary teachers and will include review of the topics within most elementary mathematics curriculum. The content areas covered will be set theory, pre-operational skills, whole number operations, estimations and mental calculation, number theory, fractions, decimals and integers, rational and real numbers, statistics, measurement, and geometry including terminology, polygons, similarity, congruence, coordinate geometry, symmetry, reflections, and notations with problem solving being emphasized throughout. Topics will be presented with appropriate styles of mathematical methodology and hands-on classroom activities. Prerequisite: sophomore, junior or senior standing.

**MTH 313 Mathematics Notation and Proof 3 Units**

This course will introduce standard mathematical notation, methods, truth tables, and principles of symbolic logic for use in determining the validity of arguments, dealing with proper notation and structure in mathematical proofs including direct and indirect proofs, mathematical induction, and construction of counter-examples. Application will be made to a field of mathematics such as set theory, algebra, or geometry. Prerequisite: C- or better in MTH 272.

**MTH 371 Linear Algebra 3 Units**

This course will study properties of matrix arithmetic, systems of linear equations, determinants, vector spaces, linear transformations, diagonalization, inner products, and applications of these topics. Prerequisite: C- or better in MTH 272.

**MTH 373 Calculus III 4 Units**

As a continuation of MTH 272, this course will include the study of vector calculus, three-dimensional calculus, partial derivatives, multiple integrals, differential calculus, and other selected topics in vector calculus. Prerequisite: C- or better in MTH 272.

**MTH 376 Discrete Mathematics 3 Units**

This course will include the study of relations and functions, graph theory, counting principles and combinatorics, set theory, Boolean algebra, code theory, linear programming, and other selected topics. Prerequisite: C- or better in MTH 271. Offered alternate years.

**MTH 379 Numerical Analysis 3 Units**

This course serves as an introduction to the basic algorithms of numerical analysis. Topics may include numerical solutions of algebraic equations, interpolation and approximation methods, approximate numerical solutions to systems of linear and non-linear equations, and numerical differentiation and integration. Prerequisite: C- or better in CSC 104 and MTH 272. Offered alternate years.

**MTH 380 Modern Geometry 3 Units**

This course will provide a general study of deductive systems of geometry including Euclidean, projective, finite, and other non-Euclidean geometries. Offered alternate years. Prerequisite: C- or better in AMTH 101 or CMTH 101 or MTH 201 or MTH 252 or MTH 271 or equivalent.

**MTH 384 Ordinary Differential Equations 3 Units**

This course will cover the classification of differential equations along with first order equations, exact differentials, integrating factors, higher order differential equations, method of undetermined coefficients, variation of parameters, operator methods, solution by infinite series, and Laplace transformations. Prerequisite: C- or better in MTH 272. Offered alternate years.

**MTH 387 Probability and Statistics I 3 Units**

This course will look at the probability and combinatorics; discrete and continuous random variables; the normal, gamma, Chi-square, Poisson, and binomial distributions with applications. Prerequisite: C- or better in MTH 373 (concurrent enrollment allowed). Offered alternate years.

**MTH 388 Probability and Statistics II 3 Units**

A continuation of MTH 387, this course will cover various multivariate probability distributions, bias and unbiased estimators, Least Square estimation, ANOVA , Block Designs, and a revisit of hypothesis testing and a study of nonparametric statistics. Prerequisite: C- or better in MTH 387. Offered alternate years.

**MTH 473 Modern Algebra I 3 Units**

This course will study the properties and operations within groups, rings, integral domains, fields, normal subgroups, quotient groups, homomorphisms, and isomorphisms. Prerequisite: C- or better in MTH 313. Offered alternate years.

**MTH 474 Modern Algebra II 3 Units**

This course is a continuation of the study of the properties and operations within rings, integral domains, fields, quotient rings, groups, subgroups, homomorphisms and isomorphisms. Prerequisite: C- or better in MTH 473 or consent of instructor. Offered alternate years.

**MTH 489 Real Analysis 3 Units**

This course will provide an introduction to the advanced study of the real number system, and the ideas and proof techniques specific to mathematical analysis. Topics include properties of the real numbers, sequences, series, limits, continuity, and differentiation. Prerequisite: C- or better in MTH 313 and MTH 373. Offered alternate years.

**MTH 495 Topics in Mathematics - Review 1.5 Unit**

As the first of two (2) capstone courses for all mathematics majors, students will meet as a group once per week to review competencies in the major, take group-wide assessments, and complete a preliminary research abstract on a topic of their choice as they work with a faculty mentor followed by a short presentation to their peers and faculty regarding their preliminary findings for reaction and feedback. Prerequisite: Senior standing.

**MTH 496 Topics in Mathematics - Final 1.5 Unit**

As the second of two (2) capstone courses for all mathematics majors, students, working with a faculty mentor, will complete their research from MTH 495 on a written project and present their findings to a committee of peers and faculty. Inclusion of the research project in the President's Academic Showcase for Undergraduate Research is encouraged. Prerequisite: Senior standing.