# Mathematics

**MTHC106 Statistics I - 4 Class Hours/4 Credits**

Without assuming a calculus background, Statistics I is an introduction to the basics of descriptive and inferential statistics. The focus of the course will be on the development of statistical literacy and statistical thinking through the examination of real-world data from a variety of contexts, including data sets that are of interest to students. Topics include statistical distributions, linear regression and correlation, surveys and experiments, sampling distributions, probability, confidence intervals and hypothesis testing. Student centered, the course engages students in projects focusing on activity-based instruction that integrates technology (e.g., dynamic statistical packaged, calculator-based "labs", spreadsheets, on-line virtual manipulative) and emphasizes the conceptual understanding of the statistical concepts studied.(Prerequisites: Minimum Accuplacer Elementary Algebra score of 78 OR successful completion (with a grade of "C" or better) of our (ISVC/ISVK016) Algebra I or (ISVC018) Fundamentals of Mathematical Literacy II, or (ISVC019) Fundamentals of Mathematical Literacy for STEM Fields OR written permission of an authorized college official (e.g., instructor, advisor, academic administrator) for students with an Accuplacer Elementary Algebra score in the range 63-77 OR written permission of Instructor.)

**MTHC107 Statistics II - 4 Class Hours/4 Credits**

Statistics II is the continuation of Statistics I. The course begins with a review of sampling distributions and topics from Statistics I as necessary. The focus of the course is on strengthening proficiency with descriptive and inferential statistics by studying topics including probability, Binomial and Geometric Distributions, confidence intervals and hypothesis testing for proportions and means, Chi-square Tests, inference for regression, and Analysis of Variance. Student centered, the course engages students in projects and case-studies and is focused on activity-based instruction that integrates technology (e.g., dynamic statistical packages, spreadsheets) and emphasizes the conceptual understanding of the statistical concepts studied. (Prerequisites: MTH106 Statistics I or equivalent; OR written permission of Instructor.)

**MTHC110 Functions & Modeling I - 4 Class Hours/4 Credits**

This course will focus on the use of functions and algebra in problem solving and modeling. Topics include the study of linear, quadratic, exponential, logarithmic, and trigonometric functions, along with translation of functions, inverse functions, and trigonometric identities. Students can expect to complete projects that involve the use of functions to model real-world behavior (e.g., the dynamics of caffeine in the body) and include topics such as data analysis, systems of linear equations, optimization, and rational functions. The course will be student centered and focus on developing quantitative literacy through activity-based instruction that integrates technology (e.g., dynamic statistical packages, calculator-based labs, spreadsheets, on-line virtual manipulatives) and emphasizes the conceptual understanding of the mathematical concepts studied. Multiple assessments tools will be used to measure the course competencies and may include on-going formative assessments, portfolios, quizzes, exams, and projects/investigations.(Prerequisites: Minimum ACCUPLACER Elementary Algebra score of 78, OR satisfactory completion (74 or higher) of Instructional Services Algebra I (ISVC016 or ISVK016), OR written permission of an authorized college official (e.g., instructor, advisor, academic administrator) for students with an ACCUPLACER Elementary Algebra score in the range 63 – 77, OR written 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.)

**MTHC114 Mathematics for the Environment - 4 Class Hours/4 Credits**

Mathematics for the Environment is a course that allows students to apply fundamental concepts in mathematics to the study of topics such as climate, economics, population growth, health care, energy and media literacy. In order to better understand the mathematics presented in these areas, students will study the language of mathematics including patterns, logic. induction, deduction, axioms, proof, number properties, relations, functions, counting techniques, combinations, and permutations. This course emphasizes quantitative literacy, writing, problem-solving skills, and habits of the mind as students engage in a critical analysis of our environment through the use of mathematics. (Co/prerequisites: Minimum ACCUPLACER Elementary Algebra score of 78, OR satisfactory completion (74 or higher) of Instructional Services Fundamentals of Mathematical Literacy II or Fundamentals of Mathematical Literacy for STEM (ISVC018, ISVK018, ISVC019, ISVK019), OR written permission of an authorized college official (e.g., instructor, advisor, academic administrator) for students with an ACCUPLACER Elementary Algebra score in the range 63-77, 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 Functions & Modeling II - 4 Class Hours/4 Credits**

Functions & Modeling II builds from Functions & Modeling I. The course will focus on strengthening proficiency with functions and modeling at both the procedural and conceptual levels to serve as a preparation for calculus. The course begins with a review of linear, quadratic, exponential, logarithmic, and trigonometric functions. Students will study inverse functions, compositions, combinations of functions, polynomial and rational functions, sequences and series, parametric equations, conic sections, and an introduction to limits and continuity. Additional topics may include complex numbers, polar coordinates, and vectors. Students can expect to complete projects that involve the use of functions to model real-world behavior and include data analysis and fitting functions to data. The course will be student centered and focus on developing quantitative literacy through activity-based instruction that integrates technology (e.g., dynamic statistical packages, computer algebraic systems, on-line virtual manipulatives) and emphasizes the conceptual understanding of the mathematical concepts studied. Multiple assessments tools will be used to measure the course competencies and may include on-going formative assessments, portfolios, quizzes, exams, and projects/investigations. (Prerequisite: 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)