# Mathematics (MATH)

### Courses

**MATH A054** Prealgebra ** 3 Credits**

Topics include operations and applications of whole numbers, integers, fractions, decimals, ratios and proportions, percents, geometry and measures, evaluation of algebraic expressions and applications. **Special Note:** MATH A054A, MATH A054B, MATH A054C combined are equivalent to MATH A054. **Registration Restrictions:** An approved UAA placement test is required.

**Prerequisites:** ALEKS Overall Test 1 with a score of 0 or ALEKS Overall Test 2 with a score of 0 or ALEKS Overall Test 3 with a score of 0 or ALEKS Overall Test 4 with a score of 0 or ALEKS Overall Test 5 with a score of 0.

**MATH A054A** Prealgebra A ** 1 Credit**

Topics include operations and applications of whole numbers, integers, fractions, decimals, ratios and proportions, and percents. The topic of math anxiety is dealt with throughout the course. **Special Note:** MATH A054A, MATH A054B, MATH A054C combined are equivalent to MATH A054. **Registration Restrictions:** An approved UAA placement test is required.

**MATH A054B** Prealgebra B ** 1 Credit**

Topics include operations and applications of integers, fractions, decimals, ratios and proportions, percents, exponents and radicals. **Special Note:** MATH A054A, MATH A054B, MATH A054C combined are equivalent to MATH A054. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A054A with a minimum grade of C.

**MATH A054C** Prealgebra C ** 1 Credit**

Topics include evaluation of algebraic expressions with applications, geometry and measures. **Special Note:** MATH A054A, MATH A054B, MATH A054C combined are equivalent to MATH A054. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A054B with a minimum grade of C.

**MATH A055** Elementary Algebra ** 3 Credits**

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. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A054 with a minimum grade of C or ALEKS Overall Test 1 with a score of 17 or ALEKS Overall Test 2 with a score of 17 or ALEKS Overall Test 3 with a score of 17 or ALEKS Overall Test 4 with a score of 17 or ALEKS Overall Test 5 with a score of 17.

**MATH A055A** Elementary Algebra A ** 1 Credit**

Topics include solutions of linear equations and graphs of lines. **Special Note:** MATH A055A, MATH A055B, MATH A055C combined are equivalent to MATH A055. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A054A with a minimum grade of C.

**MATH A055B** Elementary Algebra B ** 1 Credit**

Topics include evaluating and simplifying algebraic expressions, polynomials, factoring, and integer exponents. **Special Note:** MATH A055A, MATH A055B, MATH A055C combined are equivalent to MATH A055. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A055A with a minimum grade of C.

**MATH A055C** Elementary Algebra C ** 1 Credit**

Topics include evaluating and simplifying algebraic expressions, factoring, and quadratic equations. **Special Note:** MATH A055A, MATH A055B, MATH A055C combined are equivalent to MATH A055. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A055B with a minimum grade of C.

**MATH A060** Essential Mathematics ** 4 Credits**

Teaches the concepts of basic arithmetic and introductory algebra. Includes operations and properties on real numbers, ratio, proportion, percent, scientific notation and variation, topics from consumer mathematics, evaluation of literal expressions, solution and graphs of linear equations and inequalities; radicals and exponents, polynomials, factoring and special products, fundamental operations with algebraic fractions, solution of quadratic equations, and elementary systems of equations. Geometric formulae are presented on a case-by-case basis as needed. **Special Note:** Equivalent to MATH A054 and MATH A055. Credit will not be given for both MATH A055 and MATH A060. Placement test not required.

**Prerequisites:** ALEKS Overall Test 1 with a score of 0 or ALEKS Overall Test 2 with a score of 0 or ALEKS Overall Test 3 with a score of 0 or ALEKS Overall Test 4 with a score of 0 or ALEKS Overall Test 5 with a score of 0.

**MATH A105** Intermediate Algebra ** 3 Credits**

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. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A055 with a minimum grade of C or MATH A060 with a minimum grade of C or ALEKS Overall Test 1 with a score of 30 or ALEKS Overall Test 2 with a score of 30 or ALEKS Overall Test 3 with a score of 30 or ALEKS Overall Test 4 with a score of 30 or ALEKS Overall Test 5 with a score of 30.

**MATH A115** Art of Mathematics ** 3 Credits**

Presents practical mathematics people use, beautiful mathematics people see and abstract mathematics people dream. Enables students to describe and analyze the world around them. **Special Note:** Does not fulfill the prerequisite for any other mathematics course. **Registration Restrictions:** Placement into MATH A105 or higher and WRTG A111 or higher

**Prerequisites:** ALEKS Overall Test 1 with a score of 30 or ALEKS Overall Test 2 with a score of 30 or ALEKS Overall Test 3 with a score of 30 or ALEKS Overall Test 4 with a score of 30 or ALEKS Overall Test 5 with a score of 30.

**Attributes:** UAA Quantitative Skills GER.

**MATH A121** College Algebra for Managerial and Social Sciences ** 3 Credits**

Covers linear and quadratic equations and inequalities, algebra of matrices, introductory linear programming, exponential and logarithmic functions. Applications emphasizing the relationships of these mathematical concepts to quantitative decision making in the managerial and social sciences. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A105 with a minimum grade of C or ALEKS Overall Test 1 with a score of 55 or ALEKS Overall Test 2 with a score of 55 or ALEKS Overall Test 3 with a score of 55 or ALEKS Overall Test 4 with a score of 55 or ALEKS Overall Test 5 with a score of 55.

**Attributes:** UAA Quantitative Skills GER.

**MATH A151** College Algebra for Calculus ** 4 Credits**

Study of algebraic, logarithmic and exponential functions; systems of equations; and applications. **Special Note:** A student may apply no more than 7 credits from any combination of MATH A151, MATH A152 and MATH A155 toward the graduation requirements for any baccalaureate degree. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A105 with a minimum grade of C or ALEKS Overall Test 1 with a score of 55 or ALEKS Overall Test 2 with a score of 55 or ALEKS Overall Test 3 with a score of 55 or ALEKS Overall Test 4 with a score of 55 or ALEKS Overall Test 5 with a score of 55.

**Attributes:** UAA Quantitative Skills GER.

**MATH A152** Trigonometry ** 3 Credits**

A study of trigonometric functions, including graphing, identities, inverse trigonometric functions, solving equations and polar coordinates, and applications. **Special Note:** A student may apply no more than 7 credits from any combination of MATH A151, MATH A152 and MATH A155 toward the graduation requirements for any baccalaureate degree. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A151 with a minimum grade of C or ALEKS Overall Test 1 with a score of 65 or ALEKS Overall Test 2 with a score of 65 or ALEKS Overall Test 3 with a score of 65 or ALEKS Overall Test 4 with a score of 65 or ALEKS Overall Test 5 with a score of 65.

**Attributes:** UAA Quantitative Skills GER.

**MATH A155** Precalculus ** 5 Credits**

Covers algebra and trigonometry required for calculus. Includes polynomial, rational, exponential, logarithmic and trigonometric functions, and trigonometric identities. **Special Note:** A student may apply no more than 7 credits from any combination of MATH A151, MATH A152 and MATH A155 toward the graduation requirements for any baccalaureate degree. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A105 with a minimum grade of B or ALEKS Overall Test 1 with a score of 55 or ALEKS Overall Test 2 with a score of 55 or ALEKS Overall Test 3 with a score of 55 or ALEKS Overall Test 4 with a score of 55 or ALEKS Overall Test 5 with a score of 55.

**Attributes:** UAA Quantitative Skills GER.

**MATH A211** Mathematics for Elementary School Teachers I ** 3 Credits**

Studies elementary set theory, numeration systems, algorithms of arithmetic, elementary number theory, integers, rational numbers and problem-solving strategies. **Special Note:** MATH A211 and MATH A212 with a minimum grade of C are required to meet State of Alaska teacher certification standards.

**Prerequisites:** (MATH A121 with a minimum grade of C or MATH A151 with a minimum grade of C) and (EDSE A212 with a minimum grade of C or PSY A365 with a minimum grade of C).

**MATH A212** Mathematics for Elementary School Teachers II ** 3 Credits**

Studies functions, informal geometry, measurement, statistics and probability. **Special Note:** MATH A211 and MATH A212 with a minimum grade of C are required to meet State of Alaska teacher certification standards.

**Prerequisites:** (MATH A121 with a minimum grade of C or MATH A151 with a minimum grade of C or STAT A252 with a minimum grade of C) and (EDSE A212 with a minimum grade of C or PSY A365 with a minimum grade of C).

**MATH A221** Applied Calculus for Managerial and Social Sciences ** 3 Credits**

Covers functions and graphs, differentiation, exponential and logarithmic functions, antidifferentiation and integration, and functions of several variables. Applications of these mathematical concepts. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A121 with a minimum grade of C or MATH A151 with a minimum grade of C or ALEKS Overall Test 1 with a score of 78 or ALEKS Overall Test 2 with a score of 78 or ALEKS Overall Test 3 with a score of 78 or ALEKS Overall Test 4 with a score of 78 or ALEKS Overall Test 5 with a score of 78.

**Attributes:** UAA Quantitative Skills GER.

**MATH A251** Calculus I ** 4 Credits**

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. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** (MATH A151 with a minimum grade of C and MATH A152 with a minimum grade of C) or MATH A155 with a minimum grade of C or ALEKS Overall Test 1 with a score of 78 or ALEKS Overall Test 2 with a score of 78 or ALEKS Overall Test 3 with a score of 78 or ALEKS Overall Test 4 with a score of 78 or ALEKS Overall Test 5 with a score of 78.

**Attributes:** UAA Quantitative Skills GER.

**MATH A252** Calculus II ** 4 Credits**

Further topics in single-variable calculus, including techniques of integration, applications of integration, convergence of sequences and series, parameterized curves, and polar coordinates. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A251 with a minimum grade of C.

**Attributes:** UAA Quantitative Skills GER.

**MATH A253** Calculus III ** 4 Credits**

Multivariable calculus. Topics include vectors in two and three dimensions; differential calculus of functions of several variables; multiple integration; vector calculus, including Green's and Stokes' theorem; and applications. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A252 with a minimum grade of C.

**Attributes:** UAA Quantitative Skills GER.

**MATH A261** Introduction to Discrete Mathematics ** 3 Credits**

Introduces concepts of discrete mathematics including relations and graph theory along with prerequisite topics including sets, logic and mathematical proof. **Registration Restrictions:** If the prerequisite is not satisfied, an approved UAA placement test is required.

**Prerequisites:** MATH A151 with a minimum grade of C.

**MATH A264** Introduction to the Mathematics Major ** 1 Credit**

Introduces the major topical areas of mathematics, tools and research methods of mathematicians, and potential career paths in mathematics. Required eportfolio is begun in this course. Opportunities for undergraduates will be presented.

**Prerequisites:** MATH A251 with a minimum grade of C or concurrent enrollment or MATH A221 with a minimum grade of C or MATH A261 with a minimum grade of C.

**MATH A265** Fundamentals of Mathematics ** 3 Credits**

Studies logic, sets, relations, functions and cardinality. Introduces mathematical proof techniques.

**Prerequisites:** MATH A252 with a minimum grade of C.

**MATH A302** Ordinary Differential Equations ** 3 Credits**

Nature and origin of differential equations; analysis of first order, linear scalar, and systems of differential equations using exact, qualitative and geometric methods; forcing and resonance; Laplace transform; and applications.

**Prerequisites:** MATH A253 with a minimum grade of C.

**MATH A303** Introduction to Abstract Algebra ** 3 Credits**

Introduces groups, rings and fields.

**Prerequisites:** MATH A253 with a minimum grade of C and MATH A265 with a minimum grade of C.

**MATH A305** Introduction to Geometries ** 3 Credits**

Introduces Euclidean and non-Euclidian plane geometry and topics selected from affine geometry and projective geometry.

**Prerequisites:** MATH A253 with a minimum grade of C and MATH A265 with a minimum grade of C.

**MATH A306** Discrete Methods ** 3 Credits**

Introduces enumeration and graph theory with some algorithms.

**Prerequisites:** MATH A251 with a minimum grade of C and (MATH A261 with a minimum grade of C or MATH A265 with a minimum grade of C).

**MATH A309** Introduction to Number Theory ** 3 Credits**

Examines fundamental concepts of number theory including primes, divisibility, congruences, quadratic reciprocity, number theoretic functions, continued fractions and Diophantine equations.

**Prerequisites:** MATH A265 with a minimum grade of C.

**MATH A314** Linear Algebra ** 3 Credits**

Studies linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations, characteristic values and inner product spaces.

**Prerequisites:** MATH A253 with a minimum grade of C.

**MATH A321** Analysis of Several Variables ** 3 Credits**

Vector calculus, exterior calculus, optimization techniques, and integration with applications. Emphasizes the use of linear and multilinear algebra techniques to generalize the basic methods of calculus to several independent and dependent variables.

**MATH A324** Introduction to Real Analysis ** 3 Credits**

Investigates the limit concept with special reference to functions on the real line. Topics include continuous functions and their properties, sequences and series, and differentiation and integration of functions.

**Prerequisites:** MATH A253 with a minimum grade of C and MATH A265 with a minimum grade of C.

**MATH A371** Stochastic Processes ** 3 Credits**

Theory and applications, including moment generating functions, conditional expectation, Poisson processes, Markov chains, and topics selected from branching processes, queuing theory, random walks, and reliability theory.

**MATH A407** Mathematical Statistics I ** 3 Credits**

Topics include random variables, distribution functions, expectation and moment generating function, special parametric families of univariate distributions, joint and conditional distributions, stochastic independence, conditional expectation, distributions of functions of random variables, convergence concepts, and parametric estimation by maximum likelihood.

**MATH A408** Mathematical Statistics II ** 3 Credits**

Topics include sampling distributions, order statistics, point estimation, maximum likelihood estimators, consistency, unbiasedness, mean square error, Cramer-Rao lower bound, asymptotics of statistics, sufficient statistics, uniformly minimum variance and unbiased (UMVU) estimators, confidence intervals and hypotheses testing, lemma of Neyman Pearson, and statistical decision theory.

**Prerequisites:** MATH A407.

**MATH A410** Introduction to Complex Analysis ** 3 Credits**

Explores analytic functions, Cauchy's theorem, sequences and series, integration, and residues.

**Prerequisites:** MATH A253 with a minimum grade of C and MATH A265 with a minimum grade of C.

**MATH A420** Historical Mathematics ** 3 Credits**

Historical development of mathematical concepts in algebra, geometry, number theory, analytical geometry, calculus, probability and statistics. **Registration Restrictions:** Completion of GER Tier 1 (basic college-level skills) courses and junior or senior standing.

**Prerequisites:** MATH A253 with a minimum grade of C and MATH A265 with a minimum grade of C.

**Attributes:** UAA Integrative Capstone GER.

**MATH A422** Partial Differential Equations ** 3 Credits**

Presents analysis and solution of partial differential equations. Students will classify and solve initial and boundary value problems for elliptic, hyperbolic and parabolic types. Faculty will select additional topics.

**Prerequisites:** MATH A302 with a minimum grade of C.

**MATH A423** Advanced Engineering Mathematics ** 3 Credits**

A practical review of mathematics for engineers. Includes partial differential equations, vector and matrix analysis, Fourier analysis, and complex analysis. **Special Note:** Course does not satisfy mathematics major requirements.

**Prerequisites:** MATH A302.

**MATH A424** Advanced Engineering Mathematics: Linear and Numerical Analysis ** 3 Credits**

Emphasizes mathematics used in engineering. Includes applications of matrices, vector spaces, inner products, and linear transformations; numerical interpolation, approximation, differentiation, and quadrature; finite difference methods for ordinary and partial differential equations; and numerical stability. **Registration Restrictions:** Completion of a programming course with a minimum grade of C

**Prerequisites:** MATH A302 with a minimum grade of C and PHYS A211 with a minimum grade of C.

**MATH A425** Advanced Engineering Mathematics: Partial Differential Equations and Complex Variables ** 3 Credits**

Emphasizes mathematics used in engineering. Includes Fourier series and transforms, Bessel functions, Legendre polynomials, linear partial differential equations, and complex variables. Develops the wave, heat and potential equations via first principles. Introduces the method of characteristics as applied to shock phenomena. **Registration Restrictions:** Completion of a programming course with a minimum grade of C

**Prerequisites:** MATH A302 with a minimum grade of C and PHYS A211 with a minimum grade of C.

**MATH A426** Numerical Analysis ** 3 Credits**

Introduces numerical solutions of linear systems and eigenvalue problems, nonlinear equations and systems, numerical differentiation and integration, and numerical solutions of ordinary and partial differential equations. Introduces approximation theory, homotopy, and error and stability analysis. Provides theoretical framework for convergence analysis. **Registration Restrictions:** Completion of a programming course with a minimum grade of C.

**Prerequisites:** MATH A252 with a minimum grade of C.

**MATH A430** Concepts of Topology ** 3 Credits**

Covers axiomatic definition of a topological space, mappings between topological spaces, continuity, homeomorphism, connectivity, completeness and compactness. Also covers examples and applications from analysis and geometry. May include homotopy (the fundamental group with low-dimensional applications) and/or knot theory.

**Prerequisites:** MATH A324 with a minimum grade of C.

**Corequisites:** MATH A303.

**MATH A431** Introduction to Differential Geometry ** 3 Credits**

Develops the theory of curves and surfaces in Euclidean spaces. Presents major constructions and theorems including the Frenet-Serret apparatus, geodesics, Gauss's Theorema Egregium and the Gauss-Bonnet theorem. Introduces abstract manifolds.

**Prerequisites:** MATH A265 with a minimum grade of C and MATH A314 with a minimum grade of C.

**MATH A490A** Selected Topics in Pure Mathematics ** 1-3 Credits**

Advanced topics in mathematics selected as continuations of, or complements to, the content of upper-division undergraduate mathematics courses. Emphasis on theoretical developments. **Special Note:** Depending on topic selected, use of symbolic computation software may be required. May be repeated once for credit with a change in subtitle. **Registration Restrictions:** Instructor permission required.

**MATH A495** Mathematics Practicum ** 1-3 Credits**

Provides upper-division mathematics majors the experience of teaching mathematics. The student is responsible for 3 hours per week per credit in the mathematics laboratory. **Special Note:** May be repeated up to a maximum of 3 credits. May not be applied towards upper division elective credits for the Mathematics or Computer Science degrees. **Registration Restrictions:** Faculty permission required.

**Prerequisites:** MATH A253.

**MATH A498** Individual Research ** 1-3 Credits**

Independent research projects under the supervision of a faculty member. The result will be a paper or presentation prepared to publication standards. **Special Note:** May be repeated up to a maximum of 6 credits. **Registration Restrictions:** Minimum of 6 credits of upper division mathematics courses with a minimum grade of B and faculty permission.