Mathematics

Courses

**MATH 100 Survey of Mathematics (3 credits)**

Pre: Grade of “C” or better in MATH 25, or MATH 82, or equivalent within the past two years; placement into MATH 100; or consent of instructor.

This course covers selected mathematical topics in an effort to acquaint students with examples of mathematical reasoning. Upon successful completion of the course, students should be able to: model applied problems symbolically and perform manipulations on the symbols within an appropriate mathematical or logical formal system; distinguish between a rigorous proof and a conjecture; author an elementary proof; apply formal rules or algorithms to solve numeric, symbolic, graphical and/or applied problems; and assess the reasonableness of, then appropriately communicate, the solutions to problems. Math 100 is not intended as, and does not qualify as, a prerequisite for advanced mathematics courses. H: Through Hōkūleʻa.

**MATH 103 College Algebra (3 credits)**

Pre: Grade of “C” or better in Math 25, or MATH 82, or equivalent within the past two years; placement into MATH 103.

This course follows the elementary algebra sequence and will prepare students for pre-calculus, statistics, or other courses requiring algebraic, geometric or symbolic thinking and deduction. Students will apply algebraic and geometric techniques to solve problems, including simplifying, factoring, and/or solving radical expressions; linear, quadratic, absolute value, and literal equations; and working with inequalities, complex numbers, quadratic systems, logarithms, and introductory functions and graphs. (FS)

**MATH 103L College Algebra Lab (2 credits)**

Coreq: MATH 103M.

This lab provides in-depth guidance in problem solving, as well as instruction in collaborating with others, and developing skills to communicate mathematical ideas.

**MATH 103M College Algebra with Tutorial (3 credits)**

Pre: Grade of “C” or better in Math 24, or placement into MATH 82 or 103.

Coreq: MATH 103L.

This course follows elementary algebra I and will prepare students for pre-calculus, statistics, or other courses requiring algebraic, geometric techniques solves problems, including simplifying, factoring, and/or solving radical expressions; linear, quadratic, absolute value, and literal equations; and working with inequalities, complex numbers, quadratic systems, logarithms, and introductory functions and graphs.

**MATH 111 Math for Elementary School Teachers I (3 credits)**

Pre: Grade of C or better in MATH 103 or equivalent course work within the past two years; or placement into MATH 111; or consent of instructor.

This course is the first in the sequence of two math courses required for students in the K-6 B.Ed. degree program. Emphasis will be placed on problem solving, communication, representation, reasoning, and mathematical connections. Topics covered include operations on sets, natural numbers, integers, fractions, reals, and functions; the properties of these operations; patterns and algebra. Prospective elementary education majors only.

**MATH 112 Math for Elementary School Teachers II (3 credits)**

Pre: Completion of MATH 111 with a grade of “C” or better, or instructor consent.

This course is the second in the sequence of two math courses required for students in the K-6 B.Ed. degree program. Topics covered include operations on the natural numbers and rational numbers; properties of those operations; connections to other parts of mathematics and applications.

**MATH 115 Statistics (3 credits)**

Pre: Grade of C or better in MATH 25 or MATH 82, or higher within the past two years; placement into MATH 100; or consent of instructor.

This course encompasses an introduction to topics in statistics, including descriptive statistics, elementary probability theory, normal distributions and linear correlation, and methods of statistical inference. (FS)

**MATH 135 Pre-Calculus Elementary Functions** (3 credits)

**MATH 135 Pre-Calculus Elementary Functions**(3 credits)

Pre: Grade of “C” or better in MATH 103 or equivalent course work within the past two years; placement into MATH 135; or consent of instructor.

This course includes a variety of selected mathematical topics designed to acquaint students with a functional approach to algebra, including polynomial, exponential, and logarithmic functions; higher degree equations; inequalities; sequences; the binomial theorem; and partial fractions. This course is recommended for students pursuing further studies in buisness, economics, mathematics, and/or science-related fields.

**MATH 140 Pre-Calculus: Trigonometry & Analytic Geometry** (3 credits)

**MATH 140 Pre-Calculus: Trigonometry & Analytic Geometry**(3 credits)

Pre: Grade of “C” or better in MATH 135 or equivalent course work within the past two years; placement into MATH 140; or consent of instructor.

This course is a study of the properties of graphs of trigonometric, circular, and inverse functions; solutions of triangles; identities; solutions of trigonometric equations; conic sections; polar coordinates; and parametric equations. This course is recommended for students pursuing further studies in business, economics, mathematics, and/or science-related fields. (FS)

**MATH 140X Accelerated Pre-Calculus: Elementary Functions, Trigonometry, & Analytic Geometry ** (4 credits)

**MATH 140X Accelerated Pre-Calculus: Elementary Functions, Trigonometry, & Analytic Geometry**(4 credits)

Pre: A grade of C or better in MATH 103 or equivalent course work within the past two years; placement into MATH 140X; or consent of instructor.

This course is designed to provide an accelerated path to Calculus to students who have a strong background in College Algebra. Topics include the essential pre-calculus skills needed for success in calculus: functions, with special attention to polynomial, rational, exponential, logarithmic, and trigonometric functions; plane trigonometry; polar coordinates; and conic sections.

**MATH 241 Calculus I** (4 credits)

**MATH 241 Calculus I**(4 credits)

Pre: Grade of “C” or better in MATH 140 or equivalent course work (within the past two years); or placement into MATH 241; or instructor consent.

This course includes a variety of selected mathematical topics including limits, continuity and derivatives. Computations of derivatives---sum, product, and quotient formulas; implicit differentiation; chain-rule. Study of algebraic and trigonometric functions with the analysis of their derivatives. Linear approximation and Newton's method. Applications of derivatives to maximum-minimum problems and related rate problems. Mean-value theorem. Definite integrals and the Fundamental Theorem of Calculus. Applications of definite integrals to computations of areas, volumes, arc lengths, surface areas, etc. Simple differential equations. Simpson's rule. (FS)

**MATH 242 Calculus II** (4 credits)

**MATH 242 Calculus II**(4 credits)

Pre: Grade of “C” or better in MATH 241, or equivalent course work (within the past two years); or placement into MATH 242; or consent of instructor.

This is the second course in the calculus sequence. The course extends differentiation and integration to inverse trigonometric, logarithmic, and exponential functions, and covers such topics as basic techniques of integration, improper integrals, Taylor's series of functions and their applications and differential equations. (FS)

**MATH 243 Calculus III** (3 credits)

**MATH 243 Calculus III**(3 credits)

Pre: Grade of "C" or better in MATH 242, or equivalent course work (within the past two years); or placement into MATH 243; or consent of instructor.

Calculus III is the third course in the calculus sequence. The course covers vector algebra and geometry, vector-valued functions and motion in space, polar coordinates, differentiation in several variables, and optimization. (FS)

**MATH 244 Calculus IV** (3 credits)

**MATH 244 Calculus IV**(3 credits)

Pre: Grade of "C" or better in MATH 243, or equivalent course work (within the past two years); placement into MATH 244; or consent of instructor.

Calculus IV is the fourth course in the calculus sequence. The course covers multiple integrals, integration in vector fields, line integrals and Green’s Theorem, surface integrals, and Stokes’ and Gauss’ Theorems. (FS)

**MATH 301 Introduction to Discrete Mathematics** (3 credits)

**MATH 301 Introduction to Discrete Mathematics**(3 credits)

Pre: MATH 241, 242, 243, or 244; or instructor consent.

This course covers symbolic logic, sets, relations, functions, induction and other methods of proof, algorithms, trees, and other graphs.

**MATH 304 Mathematical Modeling: Deterministic Models** (4 credits)

**MATH 304 Mathematical Modeling: Deterministic Models**(4 credits)

Pre: MATH 242.

Deterministic mathematical modeling emphasizing models and tools used in the sciences. Mathematical topics include optimization, difference equations, and qualitative behavior solutions of differential equations. A computer lab is included.

**MATH 307 Linear Algebra and Differential Equations** (3 credits) (WI)

**MATH 307 Linear Algebra and Differential Equations**(3 credits) (WI)

Pre: Math 243 (or concurrent), or consent from the instructor.

Introduction to linear algebra, application of eigenvalue techniques to the solution of differential equations, introduction to dynamical systems and its applications, including stability of solutions, bifurcation analysis, and chaos.

**MATH 311 Introduction to Linear Algebra **(3 credits)

**MATH 311 Introduction to Linear Algebra**(3 credits)

Pre: ENG 200 and MATH 243 or concurrent; or equivalent coursework within the past two years; or instructor consent.

Algebra of matrices, linear equations, real vector spaces and transformations. Emphasis on concepts, abstraction, and instruction of careful writing. Students may receive credit for only one of MATH 307 or MATH 311.

**MATH 321 Introduction to Mathematics** (3 credits) (WI)

**MATH 321 Introduction to Mathematics**(3 credits) (WI)

Pre: ENG 200 and MATH 243 or concurrent; or equivalent coursework within the past two years; or instructor consent.

In this upper level course students are introduced to basic methods of proof that are common to many areas of mathematics. Students will learn to write mathematical proofs and may be required to do some reading without supervision. Highlights include: Euclidean geometry and number theory including classical constructions, history of calculus, foundations for analysis, polynomial equations, and set theory and logic.

**MATH 327 History of Mathematics** (3 credits) (ETH)

**MATH 327 History of Mathematics**(3 credits) (ETH)

Pre: MATH 242 or equivalent coursework within the past two years; or instructor consent. MATH 311 or MATH 321 recommended.

A historical development of mathematical techniques and ideas, including the inter-relationships of mathematics and sciences. Highlights include: Euclidean geometry and number theory including classical constructions, history of calculus, foundations for analysis, polynomial equations, and set theory and logic.

**MATH 331 Introduction to Real Analysis (3 credits)**

**MATH 331 Introduction to Real Analysis (3 credits)**

Pre: MATH 242; and MATH 321 (or concurrent); or consent of instructor.

This course encompasses the logic of mathematical proofs, completeness, topology of the plane, continuity and limits of functions, differentiation, and integration.

**MATH 351 Foundations of Euclidean Geometry (3 credits)**

**MATH 351 Foundations of Euclidean Geometry (3 credits)**

Pre: MATH 243; and MATH 321 (or concurrent); or consent of instructor.

This course covers axiomatic Euclidean geometry and an introduction to the axiomatic method, with an emphasis on writing instruction.

**MATH 371 Elementary Probability Theory** (3 credits)

**MATH 371 Elementary Probability Theory**(3 credits)

Pre: MATH 242; or consent of instructor.

This course covers sets, discrete sample spaces, problems in combinatorial probability, random variables, mathematical expectations, classical distributions, and applications.

**MATH 373** Elementary Statistics (3 credits)

**MATH 373**Elementary Statistics (3 credits)

Pre: MATH 371; or consent of instructor.

This course covers estimation, tests of significance, and the concept of power.

**MATH 411 Linear Algebra** (3 credits)

**MATH 411 Linear Algebra**(3 credits)

Pre: Grade of "B" or better in MATH 311; or consent of instructor.

This course covers vector spaces over arbitrary fields, minimal polynomials, invariant subspaces, canonical forms of matrices, unitary and Hermitian matrices, and quadratric forms.

**MATH 412 Introduction to Abstract Algebra I **(3 credits)

**MATH 412 Introduction to Abstract Algebra I**(3 credits)

Pre: MATH 311; or consent of instructor.

This course is an introduction to basic algebraic structures. Topics include: groups, finite groups, abelian groups, rings, integral domains, fields, factorization, polynomial rings, field extensions, and quotient fields with an emphasis on writing instruction. These topics are covered in the year sequence MATH 412-413.

**MATH 413** Introduction to Abstract Algebra II (3 credits)

**MATH 413**Introduction to Abstract Algebra II (3 credits)

Pre: MATH 412; or consent of instructor.

This is the second course of a year sequence and should be taken in the same academic year as MATH 412. Emphasis on writing instruction.

**MATH 480** Senior Seminar (1 credit)

**MATH 480**Senior Seminar (1 credit)

Pre: One 400-level mathematics course; or consent of instructor.

This course is a seminar for senior mathematics majors, including an introduction to methods of research. A significant portion of class time is dedicated to the instruction and critique of oral presentations. All students must give the equivalent of three presentations. Mandatory CR/NC.

**MATH -96 Selected Topics** (v 1-6)

**MATH -96 Selected Topics**(v 1-6)

Topics will vary with student interest and relevancy to the program. May be repeated for credit.

**MATH -99** Directed Reading and Research (v)

**MATH -99**Directed Reading and Research (v)

Pre: Instructor approval.

To be arranged with the instructor.