Mathematics

This 1-credit course is designed to provide additional support to students who have gaps in their math backgrounds. Students who are given a math placement score of 1 and are registered for MAT 102 will be concurrently registered for this class. Key topics from the MAT 102 curriculum will be introduced pro-actively to build a foundation for the learning that will occur in MAT 102. Topics will include, but are not limited to: exponents, factoring techniques, rational expressions, several varieties of equations, and systems of equations.

This course covers algebraic expressions and properties of exponents, factoring techniques, rational expressions, solving equations and inequalities (including linear, quadratic, absolute value, and radical), systems of equations, polynomial and rational functions, and dimensional analysis.

Topics will include: display of data, descriptive statistics, measures of central tendency, linear regression, counting, probability, random variables, expected value and variance of a random variables, discussion of gathering data, discrete probability distributions (Bernoulli, geometric, binomial), and hypothesis testing.

Specific topics will be selected that emphasize the importance of mathematical concepts and reasoning. Fundamental math skills will be developed and applied to situations and problems encountered in everyday life. Topics will typically include items such as problem-solving, logic, numeration systems, number theory, mathematical finance, geometry, fractals, and probability.

This course covers factoring techniques, operations with rational expressions, and solving various types of higher level equations and inequalities; logarithms, including exponential and logarithmic equations and their applications; circles; and trigonometric functions, including equations, identities, and applications of trigonometry.

This course covers limits and continuity; derivatives and their applications to graphing, writing equations of tangent lines, and solving related rates and optimization problems; integrals and their applications to area and volume problems.

Applications of integral calculus; techniques of integration including: (1) change of variables, (2) trigonometric substitution, (3) integration by parts, and (4) partial fractions, improper integrals, sequences, series, tests for convergence, Taylor's formula, Taylor series expansion of a function, and applications.

Parametric equations and polar coordinates, vectors and surfaces, vector-valued functions, differential calculus of functions of several variables, multiple integrals, vector calculus.

This course is the first in a sequence of two courses designed to prepare childhood, early childhood, and secondary special education majors to teach mathematics by developing a rigorous understanding of the mathematical content taught at those levels. The course will cover the concepts of arithmetic, algebra, and number theory as they relate to the elementary and middle years mathematics curriculum. Topics will include: patterns, number sets, properties of real numbers, arithmetic algorithms for operations with all types of numbers, prime factorization and its applications, operations in binary systems, ratios, proportions, percents, measurements and conversion, linear equations, and using number theory to justify mathematical relationships.

This course is the second in a sequence of two courses designed to prepare childhood, early childhood, and secondary special education majors to teach mathematics by developing a rigorous understanding of the mathematical content taught at those levels. Topics will include: probability, Venn diagrams, logical reasoning, statistical measures, and various methods of statistical graphing, geometry, similarity, transformations, and constructions. There will be emphasis on the vocabulary of mathematics and solving open ended problems using all of the skills covered in both MAT-221 and this course.

Matrix algebra, vector spaces, sub-spaces, bases for vector spaces, determinants, solving linear systems, linear transformations, change of basis, eigenvalues and eigenvectors, and applications.

This course serves as a transition to abstract mathematics. Students will learn to read and write proofs. Topics may be selected from logic, sets, proof by induction, relations, functions, cardinality, combinatorics, number theory, graph theory.

An introductory study of a specific topic in Mathematics. Intended for freshmen and sophomores, or for students with little or no background in the subject. The student may repeat the course, but not the same topic.

Basic definitions of probability and rules of probability. Counting, discrete and continuous probability distributions. Discrete and continuous joint distributions of two random variables.

This course examines aspects of the theory of ordinary differential equations and techniques of solving differential equations, including separable equations, exact equations, first order linear differential equations, and various second order linear differential equations. Linear second order differential equations with constant coefficients will be studied. Techniques for solving equations will include variation of parameters and the method of unknown coefficients. In addition, applications where differential equations model physical situations will be examined. Where appropriate, software will be used to help illustrate ideas and perform computations.

Algebraic structures, groups, rings, fields, and polynomial domains.

Axiomatic systems, finite geometries, advanced Euclidean concepts, plane hyperbolic geometry.

A rigorous treatment of the real number system and concepts from calculus. Specific topics include: the axioms of the real numbers, limits, sequences, series, convergence, continuity, differentiability, and the Riemann integral.

An in-depth, self-directed study for Junior- or Senior- level students under the guidance of a sponsoring faculty member on a planned topic that is not covered by an existing Keuka College course.

Studies from selected areas of mathematics. Written reports and formal presentations will be required. This course is considered the capstone course for students completing the mathematics major. Students may repeat the course but not the topic.

An advanced study of a specific topic in Mathematics. Intended for juniors and seniors or for students with an appropriate background in the subject. The student may repeat the course, but not the same topic.