Topics include: polynomial functions, composition of functions, inverse functions, logarithmic functions, exponential functions, linear programming, counting methods and an introduction to probability. This course will instruct using Excel as the primary technology tool.

Co-requisite lab component paired with MATH Intensive study of mathematical skills, concepts and strategies to support and supplement MATH Pre-calculus treatment of descriptive statistics, confidence intervals, hypothesis testing, simple linear regression and correlation, and basic data collection concepts. Emphasis on reasoning, interpretation, and communicating ideas in the context of a wide variety of disciplines with computer software for computations.

Carries no credit after MATH Laboratory-based course that addresses number meanings, representations, operations, algorithms, and properties. Interpreting mathematical reasoning and developing non-standard algorithms are central themes. A survey of the essentials of calculus, intended mainly for students in business and social sciences; emphasis on applications to such areas. Basic concepts and computational techniques for functions, derivatives, and integrals, with emphasis on polynomial, rational, exponential and logarithmic functions.

Very brief introduction to calculus of functions of several variables. Informal limits. Derivatives and antiderivatives, including trigonometric, exponential, and logarithmic functions. The relationship between a function, its derivative, and its antiderivative. Integration and the fundamental theorem of calculus.

Applications of calculus to physical models, geometry, approximation, and optimization. Limits and continuity. Includes elements of the theory of calculus and the language of mathematics. A continuation of MATH Techniques of integration and calculation of antiderivatives. Applications of integration to physical models, including calculation of volume, moment, mass, and centroid. Informal convergence of sequences and series of real numbers. Taylor series, Taylor polynomials, and applications to approximation.

Vectors, parametric curves, and polar coordinates. Applications of integration to physical models, including volume, moment, mass, and centroid. Convergence of sequences and series of real numbers.

## Mathematics (MATH) Courses - Undergraduate Catalogs

An introduction to the language and methods of reasoning used throughout mathematics. Topics include propositional and predicate logic, elementary set theory, proof techniques including mathematical induction, functions and relations, combinatorial enumeration, permutations and symmetry. Content drawn from propositional and predicate logic; proof logic, induction and recursion, elementary set theory; functions and relations; combinatorial enumeration; graph theory and basic elementary number theory.

Intended for computer science majors.

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Laboratory-based course that involves the study of geometry in relation to teaching secondary mathematics. Topics include: congruence, inductive and deductive reasoning, dynamic geometry technology, transformations, and applications of geometry and measurement. It is recommended that this course be taken prior to MATH Laboratory-based course that addresses the development of algebraic and proportional reasoning. Pre-calculus treatment of descriptive statistics, confidence intervals, hypothesis testing, simple linear regression, correlation, introduction to probability.

Emphasis on reasoning, problem solving, communicating ideas, and applications to a wide variety of disciplines. Use of computer statistics packages and calculators to handle computations. Laboratory-based course that addresses geometric reasoning and models, along with principles of measurement.

## Mathematics (MATH)

Interpreting mathematical reasoning, developing conjectures and sensible arguments are central themes. Laboratory-based course that addresses the statistical processes of formulating questions, collecting and analyzing data, and interpreting results.

Through activities and projects, students will use modern statistical methods while learning about social and classroom issues affecting the teaching and learning of secondary level statistics. Vector algebra and geometry, functions of several variables, partial and directional derivatives, gradient, chain rule, optimization, multiple and iterated integrals. Integrates mathematics content with the opportunity to develop proof writing and communication skills important in the mathematical sciences.

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Content is drawn from discrete and foundational math and elementary analysis. Introduction to and engagement with written and verbal communication practices characteristic to mathematical sciences. Introduction to and use of technologies that support communication in the mathematical sciences.

Solving problems from previous Putnam examinations and related problems. May be repeated once for credit. Linear algebra from a matrix perspective with applications from the applied sciences.

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## A Meaningful Math Requirement: College Algebra or Something Else?

Topics include the algebra of matrices, methods for solving linear systems of equations, eigenvalues and eigenvectors, matrix decompositions, vector spaces, linear transformations, least squares, and numerical techniques. Division algorithm. Greatest common divisor and Euclidean algorithm. Solving linear modular equations, Chinese Remainder Theorem, Primitive roots, solving modular quadratic equations. Introduction to group theory: motivation, definitions and basic properties. Introduction to security authentication, confidentiality, message integrity and non-repudiation and the mathematical mechanisms to achieve them.

Topics include concepts in cryptography and cryptanalysis, symmetric key systems, public key systems, key management, public-key infrastructure PKI , digital signatures, authentication schemes and non-repudiation. Introduction to groups, fields and polynomial rings. Group based authentication and digital signature schemes and anonymity protocols. Euclidean, non-Euclidean, and projective geometries from an axiomatic point of view. The real number system, completeness and compactness, sequences, continuity, foundations of the calculus.

Use of differential equations to model phenomena in sciences and engineering. Solution of differential equations via analytic, qualitative and numerical techniques. Linear and nonlinear systems of differential equations. Introduction to matrix algebra, determinants, eigenvalues, and solutions of linear systems. Laplace transforms. Overview of systems security: hardware, software, encryption, and physical security. Includes multiple modules: system security, physical issues in security, hardware and firmware security issues, industrial control, and all things connected to the internet.

Calculus based survey of statistical techniques used in Engineering.

### Chaffey College Mathematics Department Update

Data collection and organization, basic probability distributions, sampling, confidence intervals, hypothesis testing, process control, simple regression techniques, design of experiments. Emphasis on examples and applications to engineering, including product reliability, robust design and quality control. Calculus- based treatment of probability theory, random variables, distributions, conditional probability, central limit theorem, descriptive statistics, estimation, tests of hypotheses, and regression.

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Differs from MATH by providing more thorough coverage of theoretical foundations and wider variety of applications drawn from natural and social sciences as well as engineering. Uses Matlab and Maple software packages from a problem-oriented perspective with examples from the applied sciences. Matrix computations, solving linear systems, interpolation, optimization, least squares, discrete Fourier analysis, dynamical systems, computational efficiency, and accuracy.

Emphasis on critical thinking and problem solving using both numerical and symbolic software. Laboratory-based course that involves the study of mathematical modeling in relation to teaching secondary mathematics. The class is usually taught using collaborative learning with little or no lecture, where students work together in small groups both during and outside of class as they help each other discover and learn the material, often by exploring with hands-on objects manipulatives.

Parents of school-age children are often able to immediately apply the knowledge gained from this course to help their children understand their own studies.