Developmental, remedial and general education requirement (GER) mathematics and beginning statistics courses are offered at all three campuses of UAS; Juneau (J), Ketchikan (K) and Sitka (K). Some of these courses are offered as distance courses from the Ketchikan and Sitka campuses. All courses offered through the Juneau campus are local courses. All UAS mathematics courses are either 3 credit courses (3+0) or 4 credit courses (4+0). The same goes for UAS statistics courses, except STAT S401 which is a 4 credit course having 3 hours of lecture each week and 3 hours of computer lab each week (3+3).

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

Review of concepts necessary for a course in algebra fundamentals. Topics of study include whole numbers, integers, fractions, decimals, and applications. *Prerequisite*: Placement Test.

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

Introduction to elementary algebra including writing, simplifying and evaluating algebraic expressions; polynomials, factoring, rational forms, graphing, radicals, linear equations, linear inequalities, and problem solving. *Prerequisite*: MATH S054 with a P, or Placement test.

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

Introduction to the properties, graphs, and applications of linear, quadratic, rational, and radical functions. *Prerequisite*: MATH S055 with a C or better or Placement Test.

*MATH S106 Concepts and Contemporary **Applications of *** Mathematics:** 3 credits (3+0) J, S AA/AS GER

Study of a wide range of topics, including voting systems, management science, probability, and statistics. *Prerequisite*: MATH S105 with a C or better, or placement test.

** MATH S107 College Algebra:** 4 credits (4+0) J, K, S GER

A detailed study of linear, quadratic, rational, radical, exponential and logarithmic functions; operations on and applications of these functions, and selected topics from algebra. *Prerequisite*: MATH S105 with a C or better.

** MATH S108 Trigonometry:** 3 credits (3+0) J, K

Properties and applications of trigonometric functions. *Prerequisite*: MATH S107 with a C or better.

** MATH S200 Calculus I:** 4 credits (4+0) J, K, S GER

Limits, continuity and differentiation of functions, analysis of functions and their graphs, applications of the derivative, introduction to integration, fundamental theorem of calculus. *Prerequisite*: C or higher in both MATH S107 and MATH S108.

** MATH S201 Calculus II:** 4 credits (4+0) J

Applications of the definite integral, techniques of integration, introduction to differential equations, infinite series, polar coordinates, parametric equations, conic sections. *Prerequisite*: MATH S200 with a C or better.

** MATH S202 Calculus III:** 4 credits (4+0) J

Vectors in 3-space, vector-valued functions, differential calculus of functions of several variables, multiple integrals, vector integral calculus, Green's and Stoke's Theorem. *Prerequisite*: MATH S201 with a C or better.

** MATH S205 Mathematics for Elementary School Teachers I:** 3 credits (3+0) J

Designed for elementary education majors. Sets, functions, numeration systems, integers, elementary number theory and rational numbers. *Prerequisite*: MATH S107 with a C, or better. or STAT S107, and ED S222 with a C or better.

** MATH S206 Mathematics for Elementary School Teachers II:** 3 credits (3+0) J

Designed for elementary education majors. Real numbers, informal geometry, measurement, statistics and probability. *Prerequisite*: MATH S107 with a C or better, or STAT S107, and ED S222 with a C or better.

** MATH S215 Introduction to Proofs:** 3 credits (3+0) J

Basic techniques of abstract formal reasoning in the mathematical sciences. Topics include logic, elementary set theory, relations, functions, proof by induction and other proof techniques. Intended for students majoring in mathematics; math majors should plan to complete it concurrently with MATH 200 or 201. *Corequisite*: MATH 200.

** 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 S202 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 S200 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 S200 and MATH S215 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 S200 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 S201 and MATH 215 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 201 and 215 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 201 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 S200 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 200 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 S107.

** 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 S107 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 200 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.

Mathematics faculty advisors have a listing of the six year course sequence for mathematics and statistics courses, mathematics majors and minors are encouraged to keep close contact with their respective advisors throughout their program of study.

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

## Fall 2013

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

Study of algebraic structures including groups, rings, integral domains, and fields. *Prerequisite*: MATH S200 and MATH S215.

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

Complex numbers and their algebraic properties; functions of complex variables; calculus of complex functions; selected applications. *Prerequisites*: MATH 201.

** MATH S392 Junior Seminar** : 1 credits (1+0)

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. *Prerequisite*: MATH S201 and 215.

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

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.

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

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, or instructor permission.

## Spring 2014

** MATH S215 Introduction to Proofs** : 3 credits (3+0)

Basic techniques of abstract formal reasoning in the mathematical sciences. Topics include logic, elementary set theory, relations, functions, proof by induction and other proof techniques. Intended for students majoring in mathematics; math majors should plan to complete it concurrently with MATH 200 or 201. *Corequisite*: MATH 200

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

A thorough development of continuity, convergence of sequences and series of numbers, convergence of sequences and series of functions. *Prerequisite*: MATH S201 and MATH 215.

** MATH S392 Junior Seminar** : 1 credits (1+0)

Advanced topics in mathematics that are not found in other course offerings. Possible topics include topology, number theory, and problem solving. *Prerequisite*: MATH S201 and 215. May be repeated for credit.

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

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 200

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

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.

** 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).

## Summer 2014

To be determined.

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

Mathematics faculty advisors have a listing of the six year course sequence for mathematics and statistics courses, mathematics majors and minors are encouraged to keep close contact with their respective advisors throughout their program of study.

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

## Fall 2014

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

Linear equations, finite dimensional vector spaces, matrices, determinants, linear transformations, eigenvalues, inner product spaces. *Prerequisite*: MATH S200.

** MATH S392 Junior Seminar** : 1 credits (1+0)

Advanced topics in mathematics that are not found in other course offerings. Possible topics include topology, number theory, and problem solving. *Prerequisite*: MATH S201 and 215. May be repeated for credit.

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

*Prerequisites*: MATH 392 and departmental approval. May be repeated for credit.

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

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 200. Requires a graphing calculator.

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

*Prerequisite*

## Spring 2015

** MATH S215 Introduction to Proofs** : 3 credits (3+0)

Basic techniques of abstract formal reasoning in the mathematical sciences. Topics include logic, elementary set theory, relations, functions, proof by induction and other proof techniques. Intended for students majoring in mathematics; math majors should plan to complete it concurrently with MATH 200 or 201. *Corequisite*: MATH 200.

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

First order differential equations, higher order linear differential equations, systems of linear differential equations, power series, Laplace Transforms, numerical methods, and applications. *Prerequisite*: MATH S202 or instructor approval.

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

Selected topics from Euclidean geometry, hyperbolic geometry, elliptic geometry, projective geometry or affine geometry. *Prerequisite*: MATH S200.

** MATH S392 Junior Seminar** : 1 credits (1+0)

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. *Prerequisite*: MATH S201 and 215.

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

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. May be repeated for credit. *Prerequisites*: MATH 392 and departmental approval.

** 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).

## Summer 2015

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

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

Topics in the history of mathematics and science from antiquity to the present. *Prerequisite*: MATH S200.