# Mathematics

**Mathematics Course Placement **– *Upon admission to RVCC, all students should meet with their academic advisors to begin the mathematics course placement process. Placements are based upon multiple measures, including SAT scores and other test scores (if available), high-school transcripts, work experiences, previous college-level work, and academic focus areas. Advisors follow the Academic Advising Guide for Mathematics Courses and may subsequently refer students to a mathematics advisor for final course placements if mathematics waivers are requested.*

**MATH017R Fundamentals of Mathematical Literacy I - 2 Class Hours/2 Credits (Credits do not count toward graduation requirements.)**

Fundamentals of Mathematical Literacy I is a course that develops students' problem-solving and logical reasoning skills to prepare them for Fundamentals of Mathematical Literacy II. Topics addressed include numeracy, proportional reasoning, geometry and measurement, and equality. Upon completing Fundamentals of Mathematical Literacy I and II, students will be prepared to enter Statistics I, Mathematical Investigations, or other introductory Liberal Arts mathematics courses. The course is student centered and focuses on developing quantitative literacy skills through activity-based instruction that integrates technology (e.g., graphing technology, manipulatives) and emphasizes the conceptual understanding of the mathematical concepts studied. Much of the course will focus on the misconceptions that students have developed over their mathematical careers. Multiple assessment tools will be used to measure the course competencies and may include on-going formative assessments, portfolios, quizzes, exams, and projects/investigations. (Prerequisites: At least limited proficiency in Computations with Integers and Fractions on the diagnostic arithmetic Accuplacer exam, OR written permission of instructor or authorized Department of Instructional Services Staff or mathematics coordinator.)

**MATH018R Fundamentals of Mathematical Literacy II - 2 Class Hours/2 Credits (Credits do not count toward graduation requirements.)**

Fundamentals of Mathematical Literacy II is a course that develops students' problem-solving and logical reasoning skills to prepare them for college-level mathematics courses. Topics addressed include algebraic reasoning, graphing, linear equations and introductory statistical topics. Upon completing Fundamentals of Mathematical Literacy I and II, students wiJI be prepared to enter Statistics I, Mathematical Investigations, or other introductory Liberal Arts mathematics courses. The course is student centered and focuses on developing quantitative literacy skills through activity-based instruction that integrates technology (e.g., graphing technology, manipulatives) and emphasizes the conceptual understanding of the mathematical concepts studied. Much of the course will focus on the misconceptions that students have developed over their mathematical careers. Multiple assessments tools will be used to measure the course competencies and may include ongoing formative assessments, portfolios, quizzes, exams, and projects/investigations. (Prerequisites: (1)Successful completion ofMATH017R Fundamentals of Mathematical Literacy I (C or higher) OR (2) written permission of mathematics advisor.)

**MATH019R Fundamentals of Mathematical Literacy for STEM fields - 4 Class Hours/4 Credits (Credits do not count toward graduation requirements.)**

(STEM - Science/Technology/Engineering/Mathematics)

Fundamentals of Mathematical Literacy for STEM fields is a developmental mathematics course that develops students' problem-solving and logical reasoning skills to prepare them for college-level mathematics courses needed for STEM fields. Topics addressed include introduction to functions, polynomials, linear and quadratic functions and equations, basic geometric topics, and introductory statistical concepts. Upon completing Fundamentals of Mathematical Literacy for STEM, students will be prepared to enter Functions and Modeling I ( college-algebra and trigonometry course), or other introductory Liberal Arts mathematics courses. The course is student centered and focuses on developing quantitative literacy skills through activity-based instruction that integrates technology (e.g., graphing technology, manipulatives) and emphasizes the conceptual understanding of the mathematical concepts studied. Much of the course will focus on the misconceptions that students have developed over their mathematical careers. Multiple assessments tools will be used to measure the course competencies and may include on-going formative assessments, portfolios, quizzes, exams, and projects/investigations. (Co/Prerequisites: (1)SAT Mathematics Score 2: 450 OR (2) Successful completion (with a grade of "C" or better) of Fundamentals of Mathematical Literacy II OR (3) written permission of mathematics advisor.)

**MATH106R 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 packages, calculator-based "labs". spreadsheets, on-line virtual manipulatives) and emphasizes the conceptual understanding of the statistical concepts studied. (Prerequisites: (1) SAT Mathematics Score 2: 530 OR (2) Successful completion (with a grade of "C" or better) of Fundamentals of Mathematical Literacy II or Fundamentals of Mathematical Literacy for STEM Fields OR (3) written permission of mathematics advisor.)

**MATH107R 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: MATH106R Statistics I or equivalent; OR written permission of instructor.)

**MATH110R 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 oflinear, 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: (1) SAT Mathematics Score 2: 530 OR (2) Successful completion (with a grade of "C" or better) of Fundamentals of Mathematical Literacy II or Fundamentals of Mathematical Literacy for STEM Fields OR (3) written permission of mathematics advisor.)

**MATH112R 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 q_uestions that have remained unsolved for hundreds of years. The course is student centered and focuses on activity-based instruction that integrates technology. (Prerequisites: (1) SAT Mathematics Score 2: 530 OR (2) Successful completion (with a grade of "C" or better) of Fundamentals of Mathematical Literacy II or Fundamentals of Mathematical Literacy for STEM Fields OR (3) written permission of mathematics advisor.)

**MATH114R 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. The course emphasizes quantitative literacy, writing, problemsolving skills, and habits of the mind as students engage in a critical analysis of our environment through the use of mathematics. (Prerequisites: (1) SAT Mathematics Score 2: 530 OR (2) Successful completion (with a grade of "C" or better) of Fundamentals of Mathematical Literacy II or Fundamentals of Mathematical Literacy for STEM Fields OR (3) written permission of mathematics advisor.)

**MATH115R Finite Mathematics - 4 Class Hours/4 Credits**

Topics will include linear models, matrix theory, linear programming, combinations, and math of finance.(Prerequisites: Minimum Accuplacer Elementary Algebra score of 78 OR successful completion (74 or higher)of Instructional Services Fundamentals of Mathematical Literacy for STEM (INSV019R) 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.)

**MATH120R 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: MATH110R or Permission of Instructor)

**MATH210R Calculus I - 4 Class Hours/4 Credits**

Calculus I will focus on the study of functions, limits, derivatives and their applications, and provide an introduction to integration, along with the connection between differentiation and integration through the Fundamental Theorem of Calculus (Prerequisite: MATH120R or equivalent or Permission of Instructor)

**MATH211R Calculus II - 4 Class Hours/4 Credits**

Calculus II is the second course in single variable calculus. Major topics include integration techniques and applications, and sequences and series. Additional topics might include arc length, parametric and polar coordinates, and an introduction to differential equations. (Prerequisite: MATH210R or Permission of Instructor)

**MATH212R 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: MATH211R or Permission of Instructor)

**MATH215R 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: MATH211R or Permission of Instructor)

**MATH216R Math Language, Logic and Proof - 4 Class Hours/4 Credits**

Students will become familiar 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: MATH211R)

**MATH217R 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: MATH210R, MATH211R)

**MATH221R Ordinary Differential Equations with Linear Algebra - 4 Class Hours/4 Credits**

Ordinary Differential Equations with Linear Algebra is an introductory course in differential equations. Topics include first-order differential equations; higher-order differential equations; series solutions; The Laplace Transform; matrix algebra, Gaussian and Gauss-Jordan elimination, eigenvalues and eigenvectors; systems of linear first-order differential equations; and selected applications. Student centered, the course focuses on activity-based instruction that integrates technology and emphasizes the conceptual understanding of the concepts studied.(Prerequisite: MATH211R)