MTHC106  Statistics - 4 Class Hours/4 Credits

This course begins with a discussion of the differences between descriptive and inferential statistics. Next, the different types of data and the rudiments of statistical distributions are examined. This leads quite naturally into probability theory and probability distributions. After which much time is spent on the normal distribution and applications. Linear regression analysis is also included. The course is meant to be as experiential as possible with students doing statistics projects during the semester.(Prerequisites: Satisfactory placement test scores (Accuplacer), or successful completion of ISVC016, or permission of instructor)

MTHC110  Algebra and Trigonometry - 4 Class Hours/4 Credits

Students will begin the course with a review of linear equations and analytic geometry. Covered next will be the solution of simultaneous linear equations with applications. Polynomials and quadratics in particular will be discussed with the emphasis on roots of equations. Completing the square will be included with quadratics and conic sections will also be investigated. The course will finish with an introduction to trigonometry, inverse trig functions and some vector analysis if time permits. Much use will be made of the graphing calculator. Applications will be integrated throughout the course and particular attention will be paid to the process of problem solving. (Prerequisite: Satisfactory placement test scores (Accuplacer), or successful completion of ISVC016, or permission of instructor.)

MTHC112  Mathematical Investigations: Great Ideas in Mathematics

4 Class Hours/4 Credits

Mathematical Investigations is an introduction to various branches of mathematics, including number theory, functions and modeling, geometry, and probability and statistics. The course will focus on some of the most interesting ideas in the history of mathematics and various applications, including the infinitude of the primes, the non-denumerability of the real numbers, different sizes of infinity, golden rectangles, non-Euclidean geometry, and measuring risk. Students will complete research projects in areas such as cryptography, platonic solids, topology, chaos and fractals, and different voting methods. The course emphasizes mathematical thinking, habits of the mind, and problem solving. These strategies will allow you to apply mathematics to real-life situations. Along the way, you will confront issues that challenge your intuition and even experience mathematical questions that have remained unsolved for hundreds of years. The course is student centered and focuses on activity-based instruction that integrates technology. (Prerequisites: Satisfactory placement test scores (Accuplacer) successful completion of ISVC/K016, or written permission of instructor.)

MTHC115  Finite Mathematics - 4 Class Hours/4 Credits

Topics will include linear models, matrix theory, linear programming, combinations, and math of finance. (Prerequisites: Satisfactory placement test score, successful completion of ISVC016 or equivalent, or permission of instructor)

MTHC120  Precalculus - 4 Class Hours/4 Credits

Students will begin the course with a general discussion of the concept of a function and the inverse of a function - eventually applying these concepts to trigonometric, polynomial, and logarithmic functions. Complex variables including DeMoivre’s theorem and the connection to vectors will be discussed. Copious examples from science, technology and business will be included and the emphasis will be on critical thinking and the process of problem solving. Use of the graphing calculator will be integrated throughout the curriculum. (Prerequisites: Satisfactory placement test scores (Accuplacer), MTHC110 or permission of instructor)

MTHC210  Calculus I - 4 Class Hours/4 Credits

Calculus I will provide the student with a review of pertinent analytic geometry and functions and the concept of an inverse of a function. It will then move on to limits, differentiation, and integration. The emphasis will be on experiential learning, concepts, and problem solving. (Prerequisite: MTHC120 or equivalent or permission of instructor)

MTHC211  Calculus II - 4 Class Hours/4 Credits

Calculus II begins with a review of the major topics of differentiation rules and integration from Calculus I. Those basics are built upon by applying those rules to some transcendental functions; such as trigonometric, inverse trigonometric, and logarithmic and exponential functions. Parametric equation, infinite series, and an introduction to differential equations follow. The course is experiential by nature in that students will perform experiments that test and illuminate the theory. These experiments will help to demonstrate that the mathematics is often inspired by physical observations. Throughout the course, connections between topics will be presented and discussed. (Prerequisite: MTHC210 or permission of instructor)

MTHC212  Multivariate Calculus - 4 Class Hours/4 Credits

A course in the calculus of functions of more than one variable usually follows a year of calculus involving functions of only one variable. This course will commence with discussions of vectors and vector value functions. Partial differentiation, multiple integration, and vector operators including gradient, divergence, and curl and related integral theorems: Green’s theorem, the divergence theorem, and Stokes’ theorem will be introduced and applications will be included throughout. (Prerequisites: MTHC211 or permission of instructor)

MTHC215  Linear Algebra - 4 Class Hours/4 Credits

This course contains both the theory and computational skills needed to study vector spaces, linear transformations, diagonalization, eigenvalues and orthogonality. Students are expected to develop the ability to reason through and coherently write up proofs of theorems as well as develop computational skills. (Prerequisite: MTHC211 or permission of instructor)

MTHC216  Math Language, Logic and Proof - 4 Class Hours/4 Credits

Students will be familiarized with the language of mathematics and learn how to use it in writing mathematical proofs. Various methods of proof will be presented, and students will be expected to demonstrate a level of proficiency in their utilization. Fundamental concepts in the areas of set theory, number theory, relations and functions, and logic will be discussed and proved. (Co/prerequisite: MTHC211 or permission of instructor.)

MTHC217  Probability and Statistics - 4 Class Hours/4 Credits

This course begins with a discussion of the differences between descriptive and inferential statistics, the different types of data, and the rudiments of statistical distributions. Classical probability theory and probability distributions are discussed in general. Specific probability distributions appropriate to discrete data and continuous data are developed in detail. Estimation, hypothesis testing, and applications provide “real life” examples. Linear relationships, and regression analysis provide another means to make predictions and shoe correlations. (Prerequisite: MTHC210, MTHC211, or permission of instructor)

MTHC220  Elementary Differential Equations - 4 Class Hours/4 Credits

This first course in Differential Equations studies the theory, solutions, methods, and applications of ordinary differential equations. It includes separable variables, homogeneous equations, integrating factors, higher order differential equations, LaPlace transforms, numerical methods, and applications. (Prerequisite: MTHC211)