Developmental, remedial and general education requirement (GER) mathematics and beginning statistics courses are offered through all three campuses of UAS; Juneau (J), Ketchikan (K) and Sitka (T). Some of these courses are offered as distance courses through the Ketchikan and Sitka campuses. Except for STAT S400, all courses offered through the Juneau campus are local courses.

The following course descriptions are for mathematics and statistics courses listed in the current UAS Academic Catalog.

Mathematics Majors, see sample programs of study starting in **odd numbered fall semesters**, and **even numbered fall semesters**.

## Mathematics

Courses with an asterisk (*) are not applicable to A.A. or bachelor's degrees.

** MATH S054* Preparatory Mathematics:** 3 credits (3+0) J, K, S

Topics include operations and applications of whole numbers, integers, fractions, decimals, ratios and proportions, percents, geometry and measures, evaluation of algebraic expressions and applications. Graded Pass/Fail. Prerequisite: placement test.

** MATH S055* Elementary Algebra:** 4 credits (4+0) J, K, S

Introductory Algebra Course. Topics Include evaluating and simplifying algebraic expressions, polynomials, factoring, integer exponents, rational expressions, solutions of linear equations and inequalities, quadratic equations and graphs of lines. Prerequisite: MATH 054 with P; or placement test.

** MATH S105 Intermediate Algebra:** 4 credits (4+0) J, K, S AA/AS GER

Topics include expressions, equations and applications involving linear, quadratic, rational and radical functions; graphs of linear and quadratic functions; functions and their inverses; introduction to exponential and logarithmic functions; and systems of linear equations. Prerequisite: MATH 055 with C (2.00) or higher; or placement test.

*MATH S113 Concepts and Contemporary**Applications of*** Mathematics:** 3 credits (3+0) J, S GER

Applications of mathematics in modern society. Topics include voting systems, management science, probability and statistics. Problem solving is emphasized. Prerequisite: MATH 105 with C (2.00) or higher; or placement test.

** MATH S151 College Algebra for Calculus:** 4 credits (4+0) J, K, S GER

A detailed study of algebraic, logarithmic and exponential functions; systems of equations; applications. Prerequisite: MATH 105 with C (2.00) or higher; or placement test.

** MATH S152 Trigonometry:** 3 credits (3+0) J, K, S

A study of trigonometric functions including graphing, identities, inverse trigonometric functions, solving equations and polar coordinates; applications. Prerequisite: MATH 151 with C (2.00) or higher; or placement test.

** MATH S211 Mathematics for Elementary School Teachers I:** 3 credits (3+0) J

Designed for elementary education majors. Topics include sets, functions, numeration systems, integers, elementary number theory and rational numbers. Prerequisite: MATH 151 or STAT 107 with C (2.00) or higher.

** MATH S212 Mathematics for Elementary School Teachers II:** 3 credits (3+0) J

Designed for elementary education majors. Topics include real numbers, informal geometry, measurement, statistics and probability. Prerequisite: MATH 151 or STAT 107 with C (2.00) or higher.

** MATH S251 Calculus I:** 4 credits (4+0) J, K, S GER

A first course in single-variable calculus. Topics include limits; continuity and differentiation of functions; applications of the derivative to graphing, optimization, and rates of change; definite and indefinite integration; and the Fundamental Theorem of Calculus. Prerequisite: Both MATH 151 and MATH 152 with C (2.00) or higher; or placement test.

** MATH S252 Calculus II:** 4 credits (4+0) J

Further topics in single-variable calculus, including techniques of integration; applications of integration; convergence of sequences and series; parameterized curves; and polar coordinates. Prerequisite: MATH 251 with C (2.00) or higher.

** MATH S253 Calculus III:** 4 credits (4+0) J

Multivariable calculus. Topics include vectors in 2- and 3-dimensions; differential calculus of functions of several variables; multiple integration; vector calculus, including Green's and Stokes' Theorem; and applications. Prerequisite: MATH 252 with C (2.00) or higher.

** MATH S265 Introduction to Mathematical Proofs:** 3 credits (3+0) J

Designed for students majoring in mathematics. A study of proof techniques used in mathematics. Topics include logic, elementary set theory, relations, and functions. Prerequisite: MATH 251 with C (2.00) or higher or instructor approval.

** MATH S302 Differential Equations:** 3 credits (3+0) J

First order differential equations, higher order linear differential equations, systems of linear differential equations, power series, Laplace Transforms, numerical methods, and applications. *Prerequisite*: MATH S253 with a C or better.

** MATH S305 Geometry:** 3 credits (3+0) J

Selected topics from Euclidean geometry, hyperbolic geometry, elliptic geometry, projective geometry or affine geometry. *Prerequisite*: MATH S251 with a C or better.

** MATH S311 Modern Algebra:** 3 credits (3+0) J

Study of algebraic structures including groups, rings, integral domains, and fields. *Prerequisite*: MATH S251 and MATH S265 with C's or better.

** MATH S314 Linear Algebra:** 3 credits (3+0) J Linear equations, finite dimensional vector spaces, matrices, determinants, linear transformations, eigenvalues, inner product spaces.

*Prerequisite*: MATH S251 with a C or better.

** MATH S324 Advanced Calculus:** 3 credits (3+0) J

A thorough development of continuity, convergence of sequences and series of numbers, convergence of sequences and series of functions. *Prerequisite*: MATH S252 and MATH 265 with a C or better.

** MATH S392 Junior Seminar:** 1 credit (1+0) J

Advanced topics in mathematics that are not found in other course offerings. Possible topics include topology, number theory, and problem solving. May be repeated for credit. *Prerequisites*: MATH 252 and 265 with C's or better.

** MATH S410 Complex Variables:** 3 credits (3+0) J

Complex numbers and their algebraic properties; functions of complex variables; calculus of complex functions; selected applications. *Prerequisites*: MATH 252 with a C or better.

** MATH S411 History of Mathematics and Science:** 3 credits (3+0) J

Topics in the history of mathematics and science from antiquity to the present. *Prerequisite*: MATH S251 with a C or better.

** MATH S460 Mathematical Modeling:** 3 credits (3+0) J

Introduces the process of developing, analyzing and interpreting mathematical models. Specific areas of application will depend on student majors and/or areas of interest. Topics will be selected from applications of mathematical and statistical methods to the biological and physical sciences. Not repeatable for credit. *Prerequisites*: MATH 251 with a C or better.

** MATH S492 Senior Seminar:** 1 credit (1+0) J

Advanced topics in mathematics that are not found in other course offerings. Possible topics include topology, number theory, and problem solving. Students are required to give presentations. *Prerequisites*: MATH 392 and departmental approval. May be repeated for credit.

### Statistics

** STAT S107 Introductory Statistics:** 4 credits (4+0) S Distance Web GER

Descriptive statistics, estimations, statistical tests. *Prerequisite*: MATH S105 with grade "C" or better or placement test into MATH S151.

** STAT S273 Elementary Statistics:** 3 credits (3+0) J, K, S

Introduction to data analysis, least-squares regression, data production, sampling distributions, probability, confidence intervals, hypothesis testing. detection and analysis of patterns in data. *Prerequisite*: Math S151 or equivalent with a C or better.

** STAT S373 Probability and Statistics:** 3 credits (3+0) J

A calculus-based course emphasizing theory and applications. Continuous and discrete random variables and their probability distributions, including joint distributions; functions of random variables, including moment-generators; estimations, including Bayesian methods and maximum likelihood; introduction to the study of the power and significance of hypothesis tests. *Prerequisites*: MATH 251 with a C or better.

** STAT S400 Statistical Computing with R:** 2 credits (0+4) J Distance Web

An in-depth introduction to the fundamentals of programming with R, the free open-sourced statistical software. Emphasizes development of skills in preparing user-defined functions and code via topics introduced in traditional elementary statistics courses. Includes descriptive statistics, graphical and numerical methods for exploring univariate and bivariate data, interval estimates, one- and two-sample hypothesis tests, one-factor ANOVA, correlation, simple regression, bivariate least squares curve fitting, contingency tables, and nonparametric methods. *Prerequisite*: STAT S273 (C or higher).

** STAT S401 Regression and Analysis of Variance:** 4 credits (3+3) J

A study of multiple regression including multiple and partial correlation, the extra sum of squares principle, indicator variables, and model selection techniques. Analysis of variance and covariance for multi-factor studies in completely random and randomized complete block designs, multiple comparisons and orthogonal contrasts. *Prerequisite*: STAT S273 or equivalent or higher with a C or better, or instructor permission.

The Provost's Office maintains a *Six Year Course Sequence* for all UAS courses, **click here** to access this page.

The following upper level mathematics and statistics courses are scheduled (dependent on enrollment) to be offered at the Juneau Campus only in upcoming semesters. See the Course Descriptions, or call the mathematics faculty for more information on any course of interest.

Mathematics majors and minors should maintain close contact with their advisors throughout their program of study.

## Fall 2015

** MATH S311 Modern Algebra** : 3 credits (3+0)

** MATH S410 Complex Variables** : 3 credits (3+0)

** MATH S392/492 Mathematics Seminar** : 1 credit (1+0)

** STAT S401 Regression and Analysis of Variance** : 4 credits (3+3)

## Spring 2016

** MATH S265 Introduction to Mathematical Proofs** : 3 credits (3+0)

** MATH S324 Advanced Calculus** : 3 credits (3+0)

** MATH S392/492 Mathematics Seminar** : 1 credit (1+0)

** MATH S460 Mathematical Modeling** : 3 credits (3+0)

** STAT S400 Statistical Computing with R:** 2 credits (0+4) J Distance Web

## Summer 2016

To be determined.

The Provost's Office maintains a *Six Year Course Sequence* for all UAS courses, **click here** to access this page.

The following upper level mathematics and statistics courses are scheduled (dependent on enrollment) to be offered at the Juneau Campus only in upcoming semesters. See the Course Descriptions, or call the mathematics faculty for more information on any course of interest.

Mathematics majors and minors should maintain close contact with their advisors throughout their program of study.

## Fall 2016

* MATH S314 Linear Algebra* : 3 credits (3+0)

** MATH S392/492 Mathematics Seminar** : 1 credit (1+0)

** STAT S373 Probability and Statistics** : 3 credits (3+0)

** STAT S401 Regression and Analysis of Variance** : 4 credits (3+3)

## Spring 2017

** MATH S265 Introduction to Proofs** : 3 credits (3+0)

** MATH S302 Differential Equations** : 3 credits (3+0)

** MATH S305 Geometry** : 3 credits (3+0)

** MATH S392/492 Mathematics Seminar** : 1 credit (1+0)

** STAT S400 Statistical Computing with R:** 2 credits (0+4) J Distance Web

## Summer 2017

The following course is scheduled to be offered as demand warrants.

** MATH S411 History of Mathematics and Science** : 3 credits (3+0)