Material for Arithmetic Math 016 and Elementary Algebra Math 017 can be found on the Developmental Maths Material page.

## Math 121 Computer Mathematics and Logic

Introduction to mathematical topics pertinent to Computer Information Systems: number bases, computer coding, logic, set theory, Boolean algebra and logic gates. Prerequisite: MATH 017 or MATH 118 (or higher) placement.

Upon successful completion of this course, students will be able to:

- Convert numbers from one number base to another
- Perform basic arithmetic operations on numbers in decimal, binary and hexadecimal form.
- Construct truth tables for logical propositions and determine if two propositions are equivalent.
- Determine if a logical argument is valid
- Evaluate set theoretical expressions and determine if two sets are equal
- Determine properties of binary relations and partial orders and create matrix, diagrammatic and graphical representations of relations.
- Operate with Boolean expressions and minimize Boolean functions

## Math 123 Elementary Mathematics I

This course provides an introduction to the foundations of mathematics. Topics include: logic and sets, construction of, representation of, estimation of, algebraic, geometric, ordering and metric structures on natural numbers and whole numbers. This course is open to all students but designed primarily for future teachers. Prerequisite: MATH 118 (or higher) placement.

Upon successful completion of this course, students will be able to apply course concepts to interpret and solve problems relating to the following topics:

- Elementary logic
- Elementary set theory
- Relations
- Functions
- Numeration systems and elementary number theory

## Math 133 Elementary Mathematics II

This course is a continuation of Elementary Mathematics I. Topics include: construction of, representation of, algebraic, geometric, ordering and metric structures on rational and real numbers, approximation and estimation, elementary combinatorics, probability and statistics, notions of size, mensuration, geometric structures and symmetry. Prerequisite: MATH 123 with a grade of C or better.

Upon successful completion of this course, students will be able to apply course concepts to interpret and solve problems relating to the following topics:

- Arithmetic operations on rational and real numbers
- Numeric sense, approximation, estimation and mensuration
- Methods of counting
- Elementary probability and statistics
- Elementary geometry

## Math 137 Geometry for Design

Introduction to two- and three-dimensional geometry for students in visual design curricula. Traditional and computer-based geometrical construction; inductive and deductive reasoning; properties of triangles, polygons and circles; transformations and tessellations; area; the Pythagorean theorem; volume; similarity and the golden mean. Prerequisite: MATH 017 or MATH 118 (or higher) placement.

Upon successful completion of this course, students will be able to:

- Identify, describe, classify and compare geometric figures and objects
- Visualize and represent 2-d figures and 3-d geometric objects and develop spatial sense using computer-based technology and traditional tools of geometry
- Apply geometric properties and relationships and use geometric models to represent and solve problems and real-world applications
- Transform and tessellate geometric figures
- Understand and appreciate the historical development and application of geometry in fields such as art, architecture, design and construction.

### Sample Materials

Professor D. French

## Math 150 Introductory Data Analysis

Introduction to statistical thinking. Visual presentation of data, summarizing of data, probability, sampling and simulation. Evaluation of inferences drawn from a variety of statistical material and generation of reports summarizing and communicating statistical results. Students whose curriculum requires ECON 112/114 may not substitute MATH 150. Prerequisite: MATH 118 with a grade of C or better or MATH 161 (or higher) placement.

Upon successful completion of this course, students will be able to:

- Graph a set of one-variable data and identify symmetry, skewness, number of clusters, and outliers
- Make a scatter plot of two-variable data and use it to describe the linear correlation between the two variables
- Compute and interpret one-variable and two-variable descriptive statistics including mean, median, mode, range, interquartile range, standard deviation, variance, correlation, slope, and intercept
- Use small data sets provided to set up and test hypotheses about a population proportion using binomial probabilities.
- Algebraically manipulate statistical formulas to derive other statistical formulas

### Sample Materials

Professor S. Gramlich

Professor C. Loveridge

## Math 151 Linear Mathematics

Cartesian coordinates, linear equations in two variables, graphing lines, systems of linear equations and inequalities, Guass-Jordan elimination, matrices, matrix addition and multiplication, matrix inversion, geometric solution of linear programming problems, the Simplex method, duality. Prerequisite: MATH 118 with a grade of C or better or MATH 161 (or higher) placement.

Upon successful completion of this course, students will be able to:

- Graph lines, linear inequalities and systems of linear inequalities in the plane
- Determine whether a system of linear equations is independent, dependent or inconsistent, and solve systems of linear equations using matrices
- Solve linear programming problems graphically and using the simplex method

### Sample Material

Professor E. Koublanova

Professor C. Loveridge

Professor S. Shwe

## Math 152 Probability

Elementary set theory, counting, inclusion-exclusion, permutations and combinations, the binomial theorem, probability, sample space, events, a priori and a posteriori probability models, conditional probability, independence, discrete random variables, mean, variance, standard deviation, normal approximation to the binomial distribution. Prerequisite: MATH 118 with a grade of C or better or MATH 161 (or higher) placement

Upon successful completion of this course, students will be able to:

- Perform basic set operations
- Apply basic counting techniques to solve counting problems
- Create probability models for simple experiments and solve probability problems
- Solve problems involving probability distributions

### Sample Material

Professor S. Gramlich

Professor J. Jernigan

Professor Koublanova

## Math 153 Personal Finance

Practical introduction to basic mathematical concepts applied in the context of consumer decision making. Application of ratios, percents, powers, roots and other mathematical techniques and formulas in calculations of markup, markdown, discounts, interest compounding (earned and paid), mortgage, declining balances, depreciation, taxes payroll deductions, automobile financing, utility bills, credit card accounts, investments and savings. Prerequisite: MATH 118 with a grade of C or better or MATH 161 (or higher) placement.

Upon successful completion of this course, students will be able to:

- Solve problems in the mathematics of buying including unit prices, markup and discount.
- Solve problems involving inflation and depreciation
- Solve problems in the mathematics of taxes including sales tax, property tax and income tax
- Solve problems in the mathematics of saving including simple interest, compound interest and fixed annuities
- Solve problems in the mathematics of borrowing such as promissory notes, instalment loans, annual percentage rate, home mortgages, financing a car, credit cards, etc.

## 161 Precalculus I

Functions and relations and their graphs, transformations and symmetries; composition of functions; one-to-one functions and their inverses; polynomial functions; complex numbers; rational functions; conic sections. Prerequisite: MATH 118 with a grade of C or better

Upon successful completion of this course, students will be able to:

- Determine basic properties of functions
- Perform operations on functions
- Graph polynomial and rational functions.
- Perform operations on complex numbers
- Find real and complex roots of quadratic functions.
- Graph transformations of functions
- Graph and determine properties of conic sections

### Sample Material

Professor S. Gramlich

Professor J. Jernigan

Professor C. Loveridge

Professor D. Santos

Professor A. Schremmer

## 162 Precalculus II

Exponential and logarithmic functions, trigonometric functions, identities, inverse trigonometric functions, law of sines, law of cosines, trigonometric form of complex numbers, applications. Prerequisite: MATH 161 with a grade of C or better.

Upon successful completion of this course, students will be able to:

- Graph and determine properties of exponential and logarithmic functions.
- Graph and determine properties of trigonometric functions
- Graph and determine properties of inverse trigonometric functions
- Solve problems using trigonometric identities
- Use polar coordinates to graph polar equations
- Convert complex numbers between rectangular and polar form
- Perform operations on vectors in the plane

### Sample Material

Professor J. Brubaker

Professor J. Jernigan

Professor A. Kitover

Professor D. Santos

Professor Y. Yoo

## 163 Discrete Mathematics

Set theory; functions and relations; counting and discrete probability; introduction to graphs and trees; elements of logic; introduction to proofs, proofs by induction, direct proof and proof by contradiction; recursion; Boolean algebra and logic circuits; and applications in computer science. Number theory may also be discussed. Prerequisite: MATH 161 with a grade of C or better or MATH 162 (or higher) placement.

Upon successful completion of this course, students will be able to:

- Solve problems involving basic concepts of logic, set theory and functions
- Apply basic counting techniques to solve counting problems
- Solve problems involving mathematical induction and recurrence relations
- Determine properties of relations and use digraphs to represent relations.
- Determine properties of graphs and trees
- Use Boolean algebra to minimize logic circuits.

## 171 Calculus I

Functions, graphs, limits, continuity, derivatives and antiderivatives of algebraic and transcendental functions; techniques of differentiation; applications of derivatives, polynomial approximation; indeterminate forms; maxima and minima and applications; curve sketching; the definite integral; the fundamental theorem of calculus; integration by substitution. Prerequisite: MATH 162 with a grade of C or better.

Upon successful completion of this course, students will be able to:

- Evaluate limits of functions
- Differentiate algebraic and transcendental functions
- Solve problems involving rates of change and optimization problems
- Graph functions and determine features of graphs such as intervals of increase and decrease, concavity, inflection points, asymptotes, holes, etc
- Find anti-derivatives of functions and evaluate definite integrals using the definition of the integral and the Fundamental Theorem of Calculus
- Evaluate definite and indefinite integrals using substitution

### Sample Material

Calculus Committee

Professor J. Jernigan

Professor A. Kitover

Professor A. Schremmer

Professor Y. Yoo

## 172 Calculus II

Fundamental theorem of calculus, integration by substitution, areas and volumes, techniques of integration, arc length, improper integrals, polar coordinates and parametric equations, conic sections, sequences, infinite series, power series, convergence tests, alternating series, Taylor and Maclaurin series. Prerequisite: MATH 166 with a grade of C or better or MATH 171 with a grade of C or better.

Upon successful completion of this course, students will be able to:

- Evaluate integrals using a variety of techniques
- Solve problems involving applications of integrals such as finding areas, volumes, arc length, work, etc.
- Differentiate and integrate functions defined by parametric equations or in polar form
- Test infinite series for convergence and represent functions using power series

### Sample Material

Calculus Committee

Professor A. Kitover

Professor A Schremmer

## 251 Statistics for Science

Algebra-based statistics for science. Statistical topics include descriptive measures, graphical methods, discrete and continuous probability distributions, estimation, one- and two-tailed hypothesis testing and categorical data. Prerequisite: MATH 118 with a grade of C or better or MATH 161 (or higher) placement.

Upon successful completion of this course, students will be able to:

- Graph a set of one-variable data and identify symmetry, skewness, number of clusters, and outlier
- Make a scatter plot of two-variable data and use it to describe the linear correlation between the two variables
- Compute and interpret one-variable and two-variable descriptive statistics including mean, median, mode, range, interquartile range, standard deviation, variance, correlation, slope, and intercept
- Use probability rules, counting rules, and formulas to compute probabilities
- Compute confidence intervals and test hypotheses about proportions, means, and variances
- Algebraically manipulate statistical formulas to derive other statistical formulas

### Sample Material

Professor S. Gramlich

## 263 Discrete Mathematics II

Algorithms and algorithm efficiency; big-O, big-Ohm, big-Q and little-o notation; average and worst-case speed; sorting algorithms; graphs, adjacency and incidence matrices; paths; connectedness; bipartite graphs; isomorphism; Euler and Hamilton paths; shortest paths; Dijkstra's algorithm; Euler's formula, graph coloring; trees; prefix, infix and postfix notation; spanning trees and minimum spanning trees (Prim, Kruskal). Formal languages, finite state machines and automata may also be discussed. Only offered in spring semester and summer II session. Prerequisite: MATH 163 with a grade of C or better.

Upon successful completion of this course, students will be able to:

- Construct mathematical proofs
- Implement algorithms and evaluate their efficiency
- Work with abstract structures arising from enumeration problems in order to sort lists, traverse graphs, search for substructures with specified properties, and to code methods of solutions within suitable formal schemes
- Analyze graphs and trees combinatorially and to apply techniques of enumerating substructures of graphs and trees

## 270 Linear Algebra

Matrices, determinants, vector spaces, inner product spaces, eigenvalues, eigenvectors, linear transformations and applications. Prerequisites: MATH 171 with a grade of C or better and MATH 172 with a grade of C or better. (MATH 172 may be taken concurrently.)

Upon successful completion of this course, students will be able to:

- Solve systems of linear equations by a variety of techniques
- Represent flats in a linear space using parameters or without using parameters
- Find bases for linear spaces
- Find matrix representations of linear transformations with respect to given bases
- Compute invariants for linear maps, such as trace and determinant

### Sample Material

Professor Ji Gao

Professor D. Santos

## 271 Calculus III

Calculus of vector-valued functions and multivariate functions; vectors in multi-dimensional space; cylindrical, spherical and other coordinate systems; partial derivatives; multiple integrals; Greens Theorem; the Divergence Theorem; Stokes Theorem. Prerequisites: MATH 172 with a grade of C or better and MATH 270 with a grade of C or better.

Upon successful completion of this course, students will be able to:

- Find derivatives of maps \mathbb{R}^m \to \mathbb{R}^n}
- Compute line-integrals
- Compute surface-integrals
- Compute volume-integrals
- Use Stokes' theorem to evaluate multi-dimensional integrals

### Sample Material

Professor Ji Gao

Calculus Committee

## 272 Differential Equations

First order equations; higher order linear differential equations; systems of linear differential equations; series solutions of linear differential equations; the Laplace transform; applications; first order partial differential equations; Fourier Series. Only offered in spring semester and summer II session. Prerequisites: MATH 172 with a grade of C or better and MATH 270 with a grade of C or better.

Upon successful completion of this course, students will be able to:

- Solve special first-order equations explicitly
- Solve special second-order equations explicitly
- Solve differential equations, using Laplace-transforms
- Solve differential equations in the form of power-series
- Solve differential equations in the form of Fourier-series