# Courses Offered

**MATH 098 Algebra Review I**

*Prerequisite: Level I placement on the Basic Math Skills Inventory. (Both semesters/1 credit)*

A self-paced course designed to review basic concepts of arithmetic and elementary algebra. Topics include fractions, decimals, percents, operations with real numbers, linear equations and inequalities, graphs and functions, solving linear systems, exponents, polynomials and problem solving. Grading is on a satisfactory/unsatisfactory basis. One class and one laboratory hour.

**MATH 099 Algebra Review II**

*Prerequisite: MATH 098 or permission of instructor. (Both semesters/1 credit)*

Topics include factoring polynomials, rational expressions, absolute value equations and inequalities, radicals, rational exponents, quadratic equations and problem solving. Grading is on a satisfactory/unsatisfactory basis. One class and one laboratory hour.

**MATH 107 Fundamental Concepts of Mathematics II: Geometry, Measurement, Data Analysis, and Probability**

*Prerequisite: MATH 106. Open to early childhood education and elementary/special education majors with sophomore standing, and to others with permission of the instructor. Not intended for first-year students. (Second semester/3 credits)*

An introduction to mathematical concepts, their understanding and communication. Topics include visualization skills; basic shapes, their properties and relationships between them; communicating geometric ideas; the process of measurement; geometric concepts of length, area and volume; designing data investigations and making judgments under conditions of uncertainty. Emphasis is on developing a deep understanding of the fundamental ideas of elementary school mathematics. An integrated mathematics laboratory approach will be used, including the use of appropriate technology.

**MATH 111 Mathematics Everywhere (CORE—Foundation)**

*Prerequisite: MATH 099 or Level II placement on the Basic Math Skills Inventory or permission of the department. (Both semesters/3 credits)*

These courses promote students’ understanding and appreciation of mathematics and develop quantitative and problem solving skills. Each course uses the computer to aid in exploration and computation. Various topics are offered each semester.

**MATH 112 Applied Statistics (CORE—Foundation)**

*Prerequisite: MATH 099 or Level II placement on the Basic Math Skills Inventory or permission of the instructor. Not open to students who have received credit for ECMG 212, PSY 211 or SOC 261. (Summer and both semesters/3 credits)*

Statistics with emphasis on applications. Topics covered include statistical measures, normal distribution, sampling theory, statistical inference, hypothesis testing and quality control, correlation, regression and analysis of variance. Students will use statistical software packages on the computer to explore topics in more depth.

**MATH 120 Pre-Calculus Mathematics**

*Prerequisite: MATH 099 or Level II placement on the Basic Math Skills Inventory. Credit by exam. (Both semesters/3 credits)*

Functions and graphs: polynomial, exponential, logarithmic and trigonometric functions; analytic geometry. Emphasis is on problem-solving, mathematical modeling and the use of technology. Designed primarily as preparation for calculus.

**MATH 200L Calculus Workshop**

*Prerequisite: A course in calculus at an institution other than Hood College, either by transfer or credit by exam. May be taken concurrently with the student’s first mathematics class at Hood. This course is not open to students who have completed Math 201 at Hood. (Both semesters/1 credit)*

An introduction to the topics and tools of calculus: differential equations and initial value problems, logarithmic graphs and mathematical modeling, slope fields, population models, Euler’s Method. Mathematical and technical word processing software. Group projects and lab reports. This course is intended for students who plan to take courses beyond Calculus I at Hood, but who did not take MATH 201 here. Grading is on a satisfactory/unsatisfactory basis.

**MATH 201 Calculus I (CORE—Foundation)**

*Prerequisite: MATH 120 or Level III placement on Basic Math Skills Inventory. (Both semesters/4 credits, six hours of integrated class work and computer laboratory)*

Relationships, functions, rates of change, initial value problems, derivatives of functions of one variable, numerical solutions, applications. Emphasis is on: problem solving, collaborative work, computer exploration, writing.

**MATH 202 Calculus II**

*Prerequisite: MATH 201 or permission of the instructor. Students who did not complete MATH 201 at Hood must enroll in MATH 200L Calculus Workshop concurrently. (Both semesters/4 credits, six hours of integrated class work and computer laboratory)*

Antiderivatives and the Fundamental Theorem of Calculus; distance, velocity and acceleration; the definite integral; uses of integrals and representations of functions; distribution and density functions; Taylor polynomials and infinite series. Emphasis is on problem solving, collaborative work, computer exploration, writing.

**MATH 207 Discrete Mathematics**

*Prerequisite: MATH 120 or Level III placement on the Basic Math Skills Inventory or permission of the instructor. (Both semesters/3 credits)*

An introduction to basic concepts and techniques of discrete mathematics. Topics include logic, sets, positional numeration systems, mathematical induction, elementary combinatorics, algorithms, matrices, recursion and the basic concepts of graphs and trees. The relationship to the computer will be stressed throughout.

**MATH 304 Differential Equations**

*Prerequisite: MATH 202 or permission of the instructor. (Second semester/4 credits)*

The study and application of the ideas and techniques of calculus to the solution of real-world problems. Emphasis is on qualitative, numerical and analytic methods of solution. Extensive use of the computer.

**MATH 320 Modeling and Simulation**

*Prerequisites: MATH 112 or equivalent, MATH 202 (or transfer credit for Calculus II and MATH 200L) and MATH 207. (Second semester—even years/4 credits)*

Developing and using mathematical models to analyze and solve real-world problems. Topics will include discrete and continuous, empirical and stochastic models. Students will use computer software for analysis and simulation and will complete individual and group projects.

**MATH 333 Introduction to Abstract Mathematics**

*Prerequisites: MATH 202 and MATH 207 or permission of the instructor. (First semester/4 credits)*

An introduction to mathematical rigor and proof encountered in advanced mathematics. Topics include logic, sets, elementary number theory, relations, functions, limits, cardinality, the complex number system.

**MATH 335 Teaching Assistantship in Mathematics**

*Prerequisite: Permission of the department. May be repeated for a maximum of 4 credits. (Either semester/1 or 2 credits)*

An opportunity for students to serve as teaching and tutorial assistants for lower-division mathematics courses. Under the supervision of department faculty or The Josephine Steiner Center for Academic Achievement and Retention staff, assistants will aid students seeking to improve their mathematical skills. Grading is on a satisfactory/unsatisfactory basis.

**MATH 336 Introduction to Modern Geometry**

*Prerequisite: MATH 207 or permission of the instructor. (Second semester—odd years/ 4 credits)*

An investigation of Euclidean and non-Euclidean geometries. Use of computer technology and independent work will be an integral part of the course.

**MATH 339 Linear Algebra**

*Prerequisites: MATH 207 and MATH 202. (First semester/4 credits)*

A modern introduction to linear algebra and its applications. Emphasis on geometric interpretation, extensive use of the computer. Linear systems, matrices, linear transformations, eigenvalues and dynamical systems.

**MATH 351 Probability and Statistics**

*Prerequisites: MATH 112 and MATH 253, or permission of the instructor. (First semester—odd years/4 credits)*

A calculus-based course in the theory and application of modern probability and statistics. Topics will be chosen from the following: events and probabilities, random variables and distributions, expectation: means and variances, conditional probability and independence, generating functions and the Central Limit Theorem, hypothesis testing, point estimation, confidence intervals, linear models, ANOVA.

**MATH 375 Independent Study**

*Prerequisite: Permission of the instructor. (Either semester/1, 2 or 3 credits)*

The study of selected topics in mathematics or computing, accomplished through reading, problem assignments and projects.

**MATH 398 Mathematics Tutorial**

*Prerequisite: Permission of instructor. (Either semester/1-3 credits)*

An opportunity to work with a faculty member and a small group of students in a semester- long program of directed study.

**MATH 399 Internship in Mathematics**

*Prerequisites: 21 credits of mathematics at the 200 level or above and permission of the department. (Either semester/3 to 15 credits)*

Supervised work in applied mathematics-related projects in a governmental, private-industrial or educational setting. In order to enroll in this course, a student must meet College internship requirements. Grading is on a satisfactory/unsatisfactory basis.

**MATH 407/507 Introduction to Graph Theory**

*Prerequisite: MATH 333 or equivalent. (Second semester—odd years/3 credits)*

A rigorous study of the theory of graphs, including simple and directed graphs, circuits, graph algorithms, connectedness, planarity and coloring problems.

**MATH 409/509 Elementary Number Theory**

*Prerequisite: MATH 333. (First semester—odd years/3 credits)*

An introduction to the theory of numbers: divisibility, prime numbers, unique factorization, congruences, Euler’s phi-function, Fermat’s and Wilson’s theorems, multiplicative functions, quadratic reciprocity, perfect numbers and applications to Diophantine equations. Applications include public-key cryptography and integer arithmetic.

**MATH 440 Introduction to Abstract Algebra**

*Prerequisites: MATH 333 and 339, or permission of the instructor. (Second semester—even years/ 3 credits)*

The study of the basic structures of modern abstract algebra: groups, rings and fields. Topics include cosets, direct products, homomorphisms, quotient structures and factorization. Applications may include symmetry groups, coding theory and connections with graph theory.

**MATH 446/546 Operations Research**

*Prerequisite: MATH 320 or MGMT 312, or permission of the instructor. (Offered as needed/3 credits)*

In-depth study of operations research methods in decision theory, linear programming, distribution models, network models, dynamic programming, game theory and simulation.

**MATH 453 Introduction to Real Analysis**

*Prerequisites: MATH 253 and MATH 333, or permission of the instructor. (Second semester—odd years/3 credits)*

An introduction to real analysis and its development: infinite series, differentiability, continuity, the Riemann and Cauchy integrals, uniform convergence. Computer exploration and visualization are an essential part of the course.

**MATH 456 Numerical Analysis**

*Prerequisite: MATH 339 or permission of the instructor. (First semester—even years/4 credits)*

The theory and applications of numerical computing: interpolation and curve-fitting, solutions of algebraic and functional equations, numerical integration, numerical solutions of differential equations.

**MATH 470 Seminar: The History of Mathematics**

*Prerequisites: Senior standing and either MATH 440 or MATH 453, or permission of the department. (Second semester/3 credits)*

A seminar in the history of mathematics. Students will use primary and secondary resources, both print and nonprint, to explore the history of mathematics from pre-history to the present.

**MATH 111A The Mathematics of Daily Life (CORE—Foundation)**

*Prerequisite: Math 099 or Level II placement on the Basic Math Skills Inventory or permission of the department.(Either semester/3 credits)*

This course introduces students to a wide range of applications of mathematics to modern life. Students will learn some surprisingly simple mathematical ideas that are fundamental in the working of the modern world. Among the topics of the course are: the mathematical tools that businesses use to schedule and plan efficiently; the number codes such as UPC, ZIP codes, and ISBN codes that help organize our lives; and the surprising paradoxes and complexities of elections.

**MATH 111B The Mathematics of Democracy (CORE—Foundation)**

*Prerequisite (Either semester/3 credits)*

Students in this course will study two basic questions about democracy –“How do we vote?” and “How do we allocate power?” – from a mathematical perspective. The mathematics reveals surprising paradoxes and complications in the answers to these questions. The course explores why we vote the way we do, what problems arise in voting, and what alternatives are being tried. It will also consider how we can divide the riches of society fairly – and even what the word “fairness” could possibly mean.

**MATH 111G The Mathematics of Games and Sports (CORE—Foundation)**

*Prerequisite: MATH 099 or Level II placement on the Basic Math Skills Inventory or permission of the department (Offered once a year or by demand/3 credits)*

This course examines the serious mathematics of fun. How often should one expect to see a perfect game in Major League Baseball? Why should you always split 8s in blackjack? How can a tournament among seven teams best be scheduled? Will women ever be faster than men in the highest levels of track performance? Is it better to bet on a color or a number in roulette? Students will explore all of these questions and more using mathematical tools such as probability, linear models, and graph theory. This class also uses computational tools to solve problems and analyze data.

**MATH 112W Workshop Statistics (CORE—Foundation)**

*Prerequisite: MATH 099 or Level II placement on the Basic Math Skills Inventory. Not open to students who have received credit for ECMG 212, PSY 211 or SOC 261. (Second semester/3 credits)*

An active-learning approach to introductory statistics. Emphasis is on collaboration, discovery, exploration, use of technology. Topics covered are the same as those in MATH 112: statistical measures, distributions, sampling, inference, confidence intervals, correlation, regression, analysis of variance. Students will use a statistical software package.

**MATH 253 Multivariable Calculus**

Prerequisite: *MATH 202 or permission of instructor. Students who did not complete MATH 201 or 202 at Hood must enroll in MATH 200L Calculus Workshop concurrently. (First semester/4 credits) *

An extension of calculus to several variables. Vector calculus: vector-valued functions; speed, velocity, and curvature; parametric equations; polar coordinates; Cartesian, cylindrical, and spherical coordinate systems; vector fields and line integrals; Green's Theorem. Functions of several variables: quadric surfaces, planes, partial and directional derivatives, the gradient, double and triple integrals. Emphasis is on problem solving, collaborative work, computer exploration, writing.

**MATH 454 The Real Number System**

*Prerequisites: MATH 253 and MATH 333 (First semester—even years/1 credit)*

A theoretical development of the real number system. Properties of real numbers. Binary operations. Associative, commutative, and distributive laws. Rational and irrational numbers. Laws of exponents. Radicals. Decimal representation. This course is intended only for students enrolled in the secondary mathematics education program. A student may not receive credit for both MATH 454 and MATH 453.

**MATH 500 Statistics**

*(Summer and first semester/3 credits)*

Basic statistical methods as they apply to data and research in the human sciences and other fields. Topics include frequency distributions and their representations, measures of central tendency and dispersion, elementary probability, statistical sampling theory, testing hypotheses, non-parametric methods, linear regression, correlation and analysis of variance. Each student may be required to do a statistics project under the guidance of a cooperating faculty member in a specific discipline such as biology, economics, education, political science, psychology or sociology.

**MATH 501 Explorations in Geometry**

*Prerequisite: MATH 505 or equivalent. (Second semester—odd years/3 credits)*

This course will examine high school geometry from a more sophisticated point of view, as well as exploring more advanced Euclidean and non-Euclidean geometrics. Topics covered may include analytic geometry, spherical geometry, hyperbolic geometry, fractal geometry and transfermational geometry. Labs in Geometer’s Sketchpad will be an integral part of the course.

**MATH 502 Explorations in Algebra**

*Prerequisites: MATH 505 and a current teaching certificte. (Second semester—even years/3 credits)*

An examination of basic and advanced algebra concepts for teachers of mathematics. The course includes an introduction to the number theory and modern algebra topics that underlie the arithmetic and algebra taught in school. The focus is on collaborative learning, communication, and the appropriate use of technology, as well as on a deep understanding of algebraic theory.

**MATH 505 Discrete Mathematics**

*(Either semester/3 credits)*

Introduction to the basic mathematical structures and methods used to solve problems that are inherently finite in nature. Topics include logic, Boolean algebra, sets, relations, functions, matrices, induction and elementary recursion, and introductory treatments of combinatorics and graph theory.

**MATH 507/407 Introduction to Graph Theory**

*Prerequisites: Enrollment in the High School Track of the M.S.in Mathematics Education program or an undergraduate degree in mathematics or permission of the instructor. (Second semester—odd years/3 credits)*

A rigorous study of the theory of graphs, including simple and directed graphs, circuits, graph algorithms, connectedness, planarity and coloring problems.

**MATH 509/409 Elementary Number Theory**

*Prerequisites: Enrollment in the High School Track of the M.S.in Mathematics Education program or an undergraduate degree in mathematics or permission of the instructor. (First semester—odd years/3 credits)*

An introduction to the theory of numbers: divisibility, prime numbers, unique factorization, congruences, Euler’s phi-function, Fermat’s and Wilson’s theorems, multiplicative functions, quadratic reciprocity, perfect numbers and applications to Diophantine equations. Applications include public-key cryptography and integer arithmetic.

**MATH 546/446 Operations Research**

*Prerequisites: Enrollment in the High School Track of the M.S.in Mathematics Education program or an undergraduate degree in mathematics or permission of the instructor. (Offered as needed/3 credits)*

In-depth study of operations research methods in decision theory, linear programming, distribution models, network models, dynamic programming, game theory and simulation.

**EDMA 579 Capstone Project**

Prerequisites: Completion of 21 credits in the M.S. in Mathematics Education program. (3 credits/Either semester)

The capstone project is the culminating experience of the M.S. in Mathematics Education; it is required of each student in the high school track and recommended for students in the middle school track. Each project will focus on an idea that links mathematics to its teaching and learning. It will involve independent reading and study, reflection, writing, and perhaps action research. The capstone is assigned a letter grade, which will reflect not only the quality of the final product, but also the student’s performance throughout the project.