University of Hawaii at Hilo Catalog 2013–2014

Mathematics (MATH) Courses

College of Arts and Sciences

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Mathematics (MATH)

College of Arts and Sciences

MATH 100  Survey Of Math (3) Survey of Mathematics course is intended primarily for non-science liberal arts majors to satisfy the university's quantitative reasoning requirement. Core topics include mathematical logic and mathematical thinking and problem solving. Additional topics may include number systems, computers, algebra, and probability. Pre: None.

MATH 103  Intro to College Algebra (3) For students who need to improve algebraic skills prior to taking Pre-calculus or Applied Calculus, or for courses in Introductory Chemistry, Physics or Statistics. Topics include exponents and radicals, factoring, systems of equations, linear equations, quadratic equations, general properties of functions, graphing, polynomial functions, exponential and logarithmic functions.

MATH 104  Precalculus Math (4) MATH 104 is an intensive one semester course on the material covered in the sequence MATH 104F-104G. A student may not receive credit for both MATH 104 and MATH 104F-104G. Pre: B+ or better in MATH 103, or C or better in MATH 104F, or an appropriate recommendation on the Math Placement Test.

MATH 104F  Precal I: Functions (3) MATH 104F is the first course in a year long sequence intended to prepare students for first year calculus. Topics include general properties of functions, polynomial and rational functions, and exponential and logarithmic functions. Pre: C or better in MATH 103 or an appropriate recommendation on the Math Placement Test.

MATH 104G  Precal II: Trig & Geom (3) MATH 104G is the second course in a year long sequence intended to prepare students for first year calculus. Topics include Trigonometric functions and their properties, analytic trigonometry, an introduction to polar coordinates, parametric functions, and complex numbers. Pre: C or better in MATH 104F, or an appropriate recommendation on the Math Placement Test.

MATH 111  MS Office Tools for Math & Sci (3) Use of symbols, equations, images in scientific documents. Computations using spreadsheets with sums, averages, and scientific functions. Data analysis curve fitting, interpolation, statistics. Data presentation: visualization, charts, and graphs. Symbolic computation. Database processing: forms, queries, reports, VBA. Additional topics chosen from: real-time data acquisition, more advanced statistical methods, system simulation. Intended for science majors. Pre: Recommendation in Math Placement Test. (Same as CS 102)

MATH 115  Applied Calculus (3) (lec., lab) The course emphasis is on computations and applications to Business and Life Sciences. Topics include derivatives, curve sketching, optimization, exponential and logarithmic functions, integration and applications in these areas. Pre: C or better in MATH 103, or recommendation from the Math Placement Test.

MATH 121  Intro Stats & Prob (3) Basic topics in statistics and probability. Pre: Recommendation in Math Placement Exam.

MATH 205  Calculus I (4) (lec., lab) First half of a standard first year calculus sequence intended primarily for Natural Science majors. Topics include differential calculus, applications, and an introduction to integration. Pre: C or better in MATH 104 or MATH 104G, or an appropriate recommendation on the Math Placement Test.

MATH 206  Calculus II (4) (lec., lab) Second semester of a standard first year calculus sequence intended primarily for Natural Science majors. Topics include applications of the definite integral, techniques of integration, an introduction to differential equations, and infinite series. Pre: C or better in MATH 205.

MATH 231  Calculus III (3) Introduction to calculus of functions of several variables. Topics include partial differentiation; gradient, divergence, curl, and multi-variable optimization. Pre: C or better in MATH 206.

MATH 232  Calculus IV (3) Introduction to calculus of functions of several variables. Topics include multiple integrals, line integrals, and surface integrals; Green's Theorem and Stoke's Theorem. Pre: C or better in MATH 231.

MATH 300  Ordinary Diff Equations (3) Theory and methods of solutions of ordinary differential equations and systems of linear differential equations with constant coefficients. Power series solutions, Laplace transforms, and applications. Pre: C in MATH 206.

MATH 301  Partial Differential Equatns (3) Construction and behavior of solutions of partial differential equations in physical and engineering applications, classical equations of mathematical physics, initial and boundary value problems, and eigenvalue problems. Pre: C in MATH 300 and MATH 231. Recommended: MATH 232 or concurrent.

MATH 303  Complex Variables W/ Apps (3) Introduction to the theory of functions of a complex variable. Analytic functions, Riemann surfaces, complex integration, Taylor and Laurent series, residue theory, Cauchy-Riemann equations, Cauchy's Theorem and its applications, conformed mapping. Pre: C or better in MATH 231. Recommended: C or better in MATH 232.

MATH 304  Complex Variables W/ Apps (3) Introduction to the theory of functions of a complex variable. Analytic functions, Riemann surfaces, complex integration, Taylor and Laurent series, residue theory, conformal mapping. Applications to scientific problems of interest. Pre: MATH 303.

MATH 310  Discrete Mathematics (3) Topics from discrete mathematics, including logic, proof techniques, recurrence relations, set theory, combinatorics, relations, functions, graphs, Boolean algebraic structures and applications to coding theory. Not open to students with credit in CS 215. Pre: MATH 206.

MATH 311  Intro Linear Algebra (3) Algebra of matrices, linear equations, vector spaces, linear transformations, eigenvalue, eigenvector problems, diagonalization and basic applications. Pre: C in MATH 310 or CS 215.

MATH 314  Topology (3) A study of topological spaces and their continuous functions. A focus on properties of topologies, including compactness, Hausdorff, and connectedness. The construction of topologies, including the metric, quotient, product, and subspace topologies. Additional topics include manifold theory and functional analysis. Pre: C or better in MATH 231.

MATH 317  Intro To Theory Of Equations (3) Algebraic systems as related to solutions of polynomial equations, division algorithms and factorization for polynomials and integers, fundamental theorem of algebra, and related topics from elementary number theory including linear congruencies and rings of residue classes. Pre: C or better in MATH 310 or instructor's consent.

MATH 360  Mathematical Physics (3) Special functions of mathematical physics which arise from Sturm-Liouville equations: Bessel, beta, elliptical, gamma and Legendre functions. Generating functions, complex integral representations. Other topics may include integral transforms, Fourier analysis and linear algebra. Pre: MATH 232, or MATH 231 and 300.

MATH 380  Chaos (3) An introduction to nonlinear dynamical systems for science majors. Topics include dynamics in one and several dimensions, stability, excitable media, fractals, and time series analysis. Applications in physics, chemistry, ecology and other fields are illustrated. Pre: C or better in MATH 206 and C or better in PHYS 171 or Math 232. (Same as PHYS 380)

MATH 407  Intro To Numerical Analysis I (3) Solutions of equations in one variable, direct and iterative methods for systems of linear equations, the algebraic eigenvalue problem, interpolation and polynomial approximation, error analysis and convergence for specific methods. Offered spring semester. Pre: C in MATH 206 and MATH 311 and programming experience. (Same as CS 407).

MATH 408  Intro To Numerical Analysis II (3) A continuation of MATH 407. Topics will include approximation theory, numerical integration and differentiation, solution of systems of nonlinear equations, numerical solutions to differential equations. Pre: C in MATH 407. (Same as CS 408).

MATH 421  Elem Probability Theory (3) Sets, sample spaces, combinatorial probability, random variables, mathematical expectation, classical distributions applications. Pre: C or better in MATH 231 and concurrent registration in MATH 232.

MATH 422  Elementary Math Statistics (3) Statistical inference, estimation, hypothesis testing, regression, correlation, introduction to analysis of variance. Pre: C in MATH 421 or instructor's consent.

MATH 431  Real Analysis I (4) A study of the basic concepts and theorems underlying classical analysis, including the topology of "R", uniform convergence, and differential and integral calculus. Pre: C in MATH 232.

MATH 432  Real Analysis II (4) A study of the basic concepts and theorems underlying classical analysis, including the topology of "R", uniform convergence, and differential and integral calculus. Pre: C in MATH 232.

MATH 441  Geometry I (3) The course is specifically designed for future Math teachers. Emphasis is equally split between content and pedagogy of teaching high school Geometry. Topics include: foundations of Geometry, formal direct and indirect geometric proofs, geometric constructions, Euclidean Geometry in 2D and 3D. Pedagogy topics include: learning and practicing different teaching methods and techniques, developing lesson plans, teaching experience in a real classroom environment. Pre: C in MATH 231 and MATH 311 or instructor's consent.

MATH 442  Geometry II (3) Axiomatic system-independence and consistency, advanced concepts in Euclidean geometry, elements of non-Euclidean geometries: spherical, elliptic, hyperbolic, introduction to classical Riemann geometry and modern geometry of manifolds. Pre: C or better in MATH 441 or instructor's consent.

MATH 454  Modern Algebra I (3) Theory of groups, rings, and fields. Polynomial rings, unique factorization, and Galois Theory. Pre: C or better in MATH 310 and MATH 311 or instructor's consent. Recommended: MATH 317 and PHIL 345.

MATH 455  Modern Algebra II (3) This course is a continuation of Modern Algebra I. Pre: C or better in MATH 454.

MATH 495A  Seminar (1) Seminar presentations of topics in the physical sciences by faculty, enrolled students and invited speakers. The first semester (495A) is taken CR/NC; in the second semester (495B), students are required to present a seminar for a letter grade. Pre: senior standing or instructor’s consent. (Same as ASTR 495A-495B, GEOL 495A-495B, CHEM 495A-495B and PHYS 495A-495B.)

MATH 495B  Seminar (1) Seminar presentations of topics in the physical sciences by faculty, enrolled students and invited speakers. The first semester (495A) is taken CR/NC; in the second semester (495B), students are required to present a seminar for a letter grade. Pre: senior standing or instructor's consent. (Same as ASTR 495A-495B, GEOL 495A-495B, CHEM 495A-495B, and PHYS 494A-494B).

MATH 496  Tchg Assist & Tutoring Math (1-3) Practice in individual tutoring and in the preparation of the selected topics in mathematics lecture or laboratory courses, under direct instructional supervision. This course may be repeated for a maximum of 6 credits and may not be used for substitution for any specific course or elective requirements of Mathematics major. Pre: consent of the supervisor and the department chair.


MATH x94 Special Topics in Subject Matter (Arr.) (IO) Special topics chosen by the instructor. Course content will vary. May be repeated for credit, provided that a different topic is studied. Additional requirements may apply depending on subject and topic.

MATH x99 Directed Studies (Arr.) (IO) Statement of planned reading or research required. Pre: instructor’s consent.

Undergraduate Courses