Course Descriptions

MATH 130 - Finite Mathematics

MATH 153 - Pre-Calculus Mathematics I

• Identify and describe functions.
• Utilize functions.
• Work with prototype functions.
• Identify and describe the effects of transformations on both the algebraic and graphical forms of functions.
• Identify and describe properties of the graph of a function.

MATH 154 - Pre-Calculus Mathematics II

• Model real phenomena using trigonometric functions.
• Convert between different units of angular measure.
• Analyze the effects of transformations on the graphs of trigonometric function
• Use and manipulate inverse trigonometric functions.
• Use trigonometric formula.
• Locate and determine features of trigonometric functions and their inverses.

MATH 155 - Pre-Calculus Review (Put on reserve 9/16/17)

• Identify and describe functions.
• Utilize functions.
• Work with prototype functions.
• Identify and describe the effects of transformations on both the algebraic and graphical forms of functions.
• Identify and describe properties of the graph of a function.
• Use and manipulate inverse trigonometric functions.

MATH 164 - Foundations of Arithmetic

MATH 170 - Intuitive Calculus

MATH 172 - Calculus I

• Determine limits and continuity of functions.
• Determine the derivatives of algebraic functions using the definition of derivative.
• Determine the derivatives of functions.
• Use the concept of the derivative to determine properties of functions.
• Model situations using the derivative of a function.
• Use the first and second derivatives of a function to determine maxima and minima of a function.
• Understand the relationship between the derivative of a function and the function’s graphical representation.

MATH 173 - Calculus II

• Use the process of antidifferentiation to solve problems.
• Demonstrate an understanding of the definition of a definite integral.
• Use the Fundamental Theorem of Calcululs to solve problems.
• Compute antiderivatives using basic antidifferentiation rules.
• Use improper integrals to solve problems.
• Set up definite integrals to represent quantities that are given in context.
• Relate the techniques of integration to the solution of differential equations.

MATH 206 - Mathematics for Teachers: Number and Operations

• Identify the structure, properties, characteristics of, and relationships between ancient numeration systems and base numeration systems including the use of appropriate manipulatives to help reveal the underlying structures. 1.D.5
• Demonstrate a working knowledge of the intricacy of learning to count including the distinction between counting as a list of numbers in order and counting to determine a number of objects (cardinality principle). 1.D.4
• Use and explain arithmetic operations of different number systems and their properties through the addition, subtraction, multiplication and division of whole numbers and through the addition and subtraction of rational numbers including fraction and decimal numbers and will be able to explain and solve problems involving standard and alternative algorithms. 1.D.5
• Apply and explain the major concepts of number theory and set theory as they apply to elementary mathematics. 1.D.4, 1.D.5, 1.D.6, 4.A
• Use appropriate technology to investigate and represent concepts, methods and application of mathematical concepts. 1.D.4
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems.1.D.3
• Explain of the progression of learning that begins with the base-ten number system, counting and place value, as it builds to the understanding of and operations with whole numbers, fractions and decimal numbers. 1.D.1, 1.D.4.A, 2.A,
• Apply the fundamental principles, concepts, and procedures related to mathematical problem solving. 1.D.2, 1.D.3

MATH 207 - Mathematics Honors Seminar - Lower Level

• Name major results in a new field of mathematics.
• Locate and read modern literature in research mathematics.
• Attempt to solve open problems in mathematics.

MATH 210 - Statistics, Society, and Decisions

The statistical revolution has dramatically changed how our society makes decisions. This course will examine how statistics is used in diverse fields and current ethical and social issues surrounding the use of statistics and data.  Does not count towards the Mathematics minor. Course will be offered every year (Fall, Winter).

Prerequisites:
Prerequisite: student must have received at least a 500 on the SAT, or a 19 on the ACT or a score of 50-Pre-Algebra or 26-Algebra or 31-College Algebra or 31-Trigonometry on the Compass test or completed MATH 100B with a C or higher or a higher level math class.

Credits: (5)

Learner Outcomes:
Upon successful completion of this course, the student will be able to:

• Recognize the use of basic statistical concepts such as margins of error and p-values.
• Summarize data both graphically and numerically.
• Interpret graphical and numerical summaries of data.
• Interpret statistical concepts such as p-values and margins of error in context.
• Apply statistical concepts in varied disciplines and contexts.
• Appraise whether given statistical techniques and study designs are being applied correctly and reasonably, and whether correct conclusions are being drawn.
• Use principles of experimental design to formulate statistical questions.
• Distinguish between correlation and causation and decide when the conditions for causation have reasonably been met.
• Analyze the implications of the use of statistics and data in modern society.
• Write clear, non-technical explanations of statistical results.

MATH 216 - Number and Operations 2

• Represent proportional relationships using tables, graphs, equations, diagrams, mathematical models, and verbal descriptions.
• Demonstrate conceptual understanding in analyzing and solving real world problems that require the use of ratios, the unit rate, rates, proportions and scaling and be able to verbally and through the use of models connect proportional relationships to geometry, measurement, statistics, probability and function.
• Use and explain arithmetic operations and their properties through the addition, subtraction, multiplication and division of integers and other real numbers including irrational numbers. They will be able to explain and solve problems involving standard and alternative algorithms.
• Analyze, extend and generalize patterns both geometrically and algebraically.  They will write both in explicit and recursive definitions for generating a sequence.
• Use appropriate technology to investigate and represent concepts, methods and application of mathematical concepts.
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems.

MATH 226 - Mathematics for Teachers: Geometry and Measurement

• Use and explain geometric concepts of point, line (both parallel, perpendicular and skew), plane, and angle and use them in describing and defining shapes and reasoning about spatial locations. 1.D.8
• Explain and prove the Pythagorean Theorem and apply it to problem solving situation. 1.D.8.E
• Use and explain congruence and similarity in terms of translations, rotations, reflections and dilations and solve problems involving congruence and similarity in multiple ways.1.D.8
• Derive formulas for the perimeter and area of two dimensional figures and the volume and surface area of three dimensional figures. They will then apply the formulas to solving problems involving two and three dimensional shapes. 1.D.7, 1.D.8
• Use appropriate technology to investigate and represent concepts, methods and application of mathematical concepts. 1.D.11
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems. 1.D.2
• Using the Van Hiele levels of geometric understanding, students will explain the developmental progression of geometric thinking including the development of spatial perception, recognition of shapes, visual matching, counting, classifying and creation of two- and three-dimensional objects, creating and expanding patterns, and spatial rotation. 1.D.1, 2.A
• Engage in developmentally and culturally responsive teaching of geometric concepts. 1.D.12.E, 2.B, 2.C, 2.D, 4. A, 4.B, 4.C
• Select, use, and determine suitability of the available mathematics curricula, teaching materials, and other resources including manipulatives for the teaching/learning of geometry for all students. 1.D.12.A, 2.B, 2.C, 2.D, 4. A, 4.B, 4.C
• Demonstrate the ability to guide student discourse with geometric concepts. 1.D.12.C, 4.I

MATH 232 - Discrete Modeling for Middle-level Teachers

• Use and apply the process of mathematical induction
• Use and apply different types of counting principles
• Use and apply recurrence relation principles.
• Use and apply deductive logic as a form of reasoning
• Use and apply models having roots in graph theory, combinatorics, linear programming, and difference equations.
• Create and teach a problem solving discrete mathematics lesson using pedagogy appropriate for middle level students.

MATH 237 - Ciphers and Mathematics

• Encrypt and decrypt monoalphabetic substitution ciphers.
• Use mathematical techniques (frequency analysis, word lengths, and linguistic patterns) to cryptanalyze monoalphabetic substitution ciphers.
• Encrypt and decrypt transposition ciphers.
• Determine and use appropriate mathematical techniques to cryptanalyze transposition ciphers.
• Encrypt and decrypt Vigenere Cipher.
• Apply frequency analysis, Kaisiski method, and the index of coincidence to cryptanalyze Vingere ciphers.

MATH 250 - Intuitive Geometry for Elementary Teachers

MATH 251 - Probability and Statistics for Elementary Teachers (Put on reserve 9/16/17)

• Formulate questions that can be addressed with data.
• Collect, organize and display data using a variety of methods and representations.
• Select and use appropriate statistical methods to analyze data.
• Develop and evaluate inferences and predictions that are based on data.
• Understand and apply basic concepts of probability.
• Conduct simulations and be able to calculate probabilities from these simulations.

MATH 260 - Sets and Logic

• Perform basic set operations and determine set relations.
• Interpret and manipulate quantified statements in mathematical notation.
• Analyze the structure of mathematical arguments and proofs.
• Construct mathematical proofs.
• Disprove a statement.

MATH 265 - Linear Algebra I

• Solve systems of linear equations.
• Perform basic matrix operations.
• Determine and use vector space properties.
• Translate information between the context of systems of equations, coefficient matrices, and the domain and range of a linear transformation.
• Solve problems requiring the use of eigenvalues and eigenvectors.

MATH 272 - Multivariable Calculus I

• Compute partial sums.
• Determine convergence and values of infinite series.
• Determine the interval of convergence for power series.
• Solve problems using Taylor Polynomials and Taylor Series.
• Learn basic vector algebra properties in R”2 and R”3.
• Solve problems using functions of two or more variables.
• Solve problems requiring partial differentiation of functions in two or more variables.

MATH 273 - Multivariable Calculus II

• Use double and triple integrals to solve problems.
• Use parametric descriptions of curves and surfaces.
• Use vector fields to solve problems.
• Use line integrals to solve problems.
• Use surface integrals to solve problems.
• State and apply the Divergence and Stoke’s theorems to solve problems.
• Use line integrals to solve problems.

MATH 298 - Special Topics

MATH 299 - Seminar

MATH 299E - Orientation Seminar: Secondary Mathematics

MATH 299S - Seminar - Math Major Orientation

MATH 306 - Middle-level Mathematics Standards Review

• Use and explain concepts from the six mathematical content domains of the Common Core State Standards for middle level mathematics.
• Use and explain the mathematical practices Common Core State Standards for middle level mathematics.
• perform mathematical tasks that reflect on the philosophical and pedagogical practices of the teaching of mathematics in our present culture.
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems.
• Use appropriate technology to investigate and represent concepts, methods and application of mathematical concepts

MATH 311 - Statistical Concepts and Methods

MATH 314 - Probability and Statistics

• Apply the basic rules of probability to calculate probabilities.
• Calculate probabilities and moments for continuous and discrete distributions.
• Use sampling distributions and limit theorems to calculate probabilities for sample means and proportions.
• Apply confidence intervals, hypothesis intervals, and other statistical tools to real data sets.
• Decide on the appropriate statistical tool for a given situation, and defend the use of that particular tool.
• Write statistical problems and results clearly and correctly.

MATH 316 - Mathematics for Teachers: Proportional Reasoning and Algebra

• Represent proportional relationships using tables, graphs, equations, diagrams, mathematical models, and verbal descriptions. 1.D.10
• Demonstrate conceptual understanding in analyzing and solving real world problems that require the use of ratios, the unit rate, rates, proportions and scaling and be able to verbally and through the use of models connect proportional relationships to geometry, measurement, statistics, probability and function. 1.D.4
• Use and explain arithmetic operations and their properties through the addition, subtraction, multiplication and division of integers and other real numbers including irrational numbers. They will be able to explain and solve problems involving standard and alternative algorithms. 1.D.5
• Analyze, extend and generalize patterns both geometrically and algebraically.  They will write both explicit and recursive definitions for generating a sequence. 1.D.6
• Use appropriate technology to investigate and represent concepts, methods and application of mathematical concepts 1.D.11
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems. 1.D.2
• Demonstrate the ability to embed CCSS-M Mathematical Practices in the instructional process to deepen conceptual understanding. 1.D. 3, 4.A, 4.B
• Select, use, and determine suitability of the available mathematics curricula, teaching materials, and other resources including manipulatives for the learning of mathematics for all students. 1.D.12.A, 4.A, 4.B, 4.C, 4.F, 4.H
• Demonstrate the ability to guide student discourse in mathematical problem solving, argumentation (creation and critiquing), literacy, and in-depth conceptual understanding. 1.D.12.C, 4.A, 4.B, 4.C, 4.D, 4.E, 4.I
• Demonstrate knowledge of learning progressions, including conceptual and procedural milestones and common misconceptions, within each content domain and connections to instruction. 1.D.12.D, 2.A, 4.A
• Engage in developmentally and culturally responsive teaching of mathematics 1.D.12.E, 2.C, 2.D, 3.D, 4.A, 4.B, 4.D,
• Design and implement a wide range of assessment strategies to inform mathematics instruction and support student learning. 5.A, 5.B, 5.C, 5.D, 5. E, 5.F

MATH 320 - History of Mathematics

MATH 321 - Math WEST-E Prep

• Demonstrate understanding of mathematical processes of reasoning and proof, mathematical communication, problem solving, and connections and mathematical history.
• Demonstrate understanding of number representations, mathematical operations, and basic number theory.
• Demonstrate understanding of algebraic and trigonometric functions, as well as linear algebra.
• Demonstrate understanding of measurement, axiomatic systems, Euclidean geometry, coordinate and transformational geometry, and non-Euclidean geometry.
• Demonstrate understanding of principles of probability, statistics and discrete mathematics.
• Demonstrate understanding of principles of calculus.

MATH 322 - Assessment of Student Learning for Mathematics Teachers

• Work with individual or small groups of students will analyze student work to identify error patterns in math content and language and implement teaching strategies to support their individual needs.
• Will plan and implement a learning segment (at least three days of planning instruction and assessment). Instruction activities, assessment activities, and state standards/targets must be aligned and multiple assessment strategies must be used.
• As part of the learning segment teacher candidates will use the assessment information to modify next lessons and target support for students who are struggling to meet the learning targets.
• As part of the learning segment teacher candidates will provide students with feedback on what they did correctly and incorrectly as well as guidance for improving their ability to meet the learning targets.
• Make appropriate adjustments to instruction during the learning segment from monitoring student learning as well as their own teaching practices.

MATH 323 - Teaching Middle-level Mathematics

• Plan and implement a learning segment (at least two days of planning instruction and assessment) based on the learner characteristics and school context of a local 4-9 mathematics classroom.
• appropriately choose concrete materials (manipulatives) and technology to plan and teach lesson in which students develop a deep understanding of mathematical ideas.
• Plan and implement a classroom management plan based on learner characteristics and school context for a local 4-9 mathematics classroom. The plan will include rationale for strategies that will promote student learning, encourage collaboration, cooperation, positive social interaction, conflict resolution skills, individual and group motivation, and value each learner’s unique contributions.
• Participation in professional mathematics organizations and use printed and on-line resources.

MATH 324 - Methods and Materials in Mathematics-Secondary

• Plan and implement a learning segment (at least three days of planning instruction and assessment) based on the learner characteristics and school context of a local 6-12 mathematics classroom.
• Appropriately choose concrete materials (manipulatives) and technology media to plan and teach lesson were students develop a deep understanding of mathematical ideas.
• Plan and implement a classroom management plan based on learner characteristics and school con text for a local 6-12 mathematics classroom. The plan will include rationale for strategies that will promote student learning; encourage collaboration, cooperation, positive social interaction, conflict resolution skills, and individual and group motivation; and value each learner’s unique contributions.
• Demonstrate their participation in professional mathematics organizations and the use of their printed and on-line resources.

MATH 325 - Instructional Practices for Teaching Mathematics

• Use technology to engage student in problem solving and collaborating with others.
• Plan, teach, and video- tape a lesson taught. The candidate will demonstrate their ability to offer structured opportunities for students to develop their own understanding of mathematical concepts, problem-solving strategies, and reasoning.
• As demonstrated in the video clip of the lesson they taught, the teacher candidates must demonstrate their ability to facilitate students’ responses and actions to improve their understanding of mathematical concepts and make mathematical connections.
• Create a web-site as a resource for them and other mathematics teachers. This site will demonstrate the candidate’s ability to use technology to engage students in problems solving, support student learning to struggling students, model and promote digital citizenship, and to use the National Education Technology Standards for Teachers to improve their teaching.

MATH 330 - Discrete Mathematics

MATH 331 - Continuous Models

• SWBAT calculate symbolically and numerically, multiple integrals.
• SWBAT model physical applications with multiple integrals.
• SWBAT model physical applications with line integrals.
• SWBAT solve simple linear differential equations of the first and second orders.
• SWBAT model physical situations with linear differential equations of the first and second orders.

MATH 332 - Discrete Models

• Use and apply the process of mathematical induction
• Use and apply different types of counting principles
• Use and apply algebraic and linear algebraic properties and principles.
• Use and apply deductive logic as a form of reasoning
• Use and apply models having roots in graph theory, combinatorics, difference equations, and social choice.

MATH 335 - Combinatorics and Graph Theory

• Compute and compare cardinalities of different sets.
• Categorize graphs.
• Synthesize symbolic and graphical representations of graphs to create proofs.
• Construct correct mathematical proofs, as well as criticize proofs.

MATH 337 - Cryptological Mathematics

• Demonstrate a mathematical understanding of various substitution ciphers.
• Demonstrate an understanding of Hill ciphers.
• Demonstrate an understanding of the Vigenere Cipher.
• Demonstrate an understanding of the number theory behind the RSA encryption/decryption algorithms.

MATH 351 - Point Set Topology

• Use definition of topology to determine what collections are topologies.
• Test functions to determine their continuity.
• Construct correct proofs utilizing axioms and definitions of topology.
• Formulate necessary and/or sufficient conditions guaranteeing the truthfulness of mathematical statements.

MATH 355 - College Geometry I

• Utilize inductive and deductive reasoning in the development of geometric notions.
• Utilize the concepts of finite geometries to understand the concept of axiomatic.
• Utilize the concepts of Euclidean geometry in its coordinate free form.
• Utilize the concepts of Euclidean geometry in its coordinate form.
• Utilize the concepts of Euclidean transformations and their respective invariants in heuristic, coordinate free, and coordinated forms.
• Utilize the concepts of equivalence relations and equivalence classes to identify similar geometric objects.
• Utilize technology appropriately to examine, explore, expand, and explain the concepts of Euclidean Geometry.

MATH 360 - Algebraic Structures I

• Analyze set structures to determine whether these structures are Abelian groups.
• Analyze set functions to determine whether the functions have homomorphic and isomorphic structures.
• Distinguish between dihedral groups of transformations and more general permutation groups.
• Demonstrate Cayley’s Theorem
• Demonstrate the Fundamental Homomorphism Theorem
• Demonstrate proofs of elementary theorems of Group Theory

MATH 361 - Algebraic Structures II

• Utilize the common modules, rings, and fields and their representations.
• Utilize abstract reasoning in both deductive and inductive forms.
• Utilize connections among the abstract notions of modules, rings, and fields and other areas of mathematics and science.
• Utilize the algebraic structure associated with modules, rings, and fields, including chains, extensions, products, and tensor products.
• Utilize the functional and structural relationships among groups and between groups and other algebraic structures.

MATH 365 - Linear Algebra II

• Describe general vector spaces and their subspaces, besides subsets of R^n.
• Use properties of abstract vector spaces.
• Employ properties of linear transformations defined on abstract vector spaces.
• Relate coordinates with respect to different bases of abstract vector spaces.
• Write proofs using standard mathematical techniques.

MATH 371 - Advanced Calculus

• Recognize standard analytical definitions such as supremum, infimum, and convergence.
• Use the definition of continuity to determine whether or not functions are continuous using various definitions of continuity.
• Examine sequences and series and determine their convergence.
• Write correct proofs using standard mathematical techniques.
• Estimate quantities using the triangle inequality to show convergence.

MATH 372 - Complex Analysis (Put on Reserve 9/16/16.)

• Differentiate the elementary functions, compute line integrals, compute real integrals using residues and Cauchy’s Theorem, compute the Taylor series for a holomorphic function and the radius of convergence for its Taylor series.
• Determine where a region is mapped to under a linear fractional transformation. Conversely, students will be able to define a linear fractional transformation that maps one region to another region.
• Prove a given function is holomorphic using the Cauchy-Riemann equations.
• Give an epsilon-delta continuity proof.

MATH 376 - Differential Equations I

• Apply existence and uniqueness theorems to initial value problems.
• Formulate initial value problems.
• Solve differential equations using analytic methods.
• Analyze differential equations using numerical software.
• Describe both analytic and approximate solutions clearly using appropriate mathematical notation and language.

MATH 377 - Differential Equations II

• Formulate initial value problems involving systems of differential equations.
• Solve initial value problems involving systems of differential equations using standard techniques.
• Graphically describe solutions for two- dimensional autonomous systems of differential equations.
• Identify important properties of non- linear systems of differential equations.
• Analyze systems of differential equations using numerical software.
• Describe both analytic and approximate solutions clearly using appropriate mathematical notation and language.

MATH 396 - Individual Study

MATH 397 - Honors

MATH 398 - Special Topics

MATH 399 - Seminar

MATH 405 - Probability and Statistics for Teachers

• Read, interpret and make decisions based upon data from graphical displays, such as line graphs, box and whisker plots, histograms, bar graphs, dot plots and scatter plots.
• Use and explain various ways to summarize, describe and compare distributions of numerical data in terms of shape center and spread.
• Calculate and explain theoretical and experimental probabilities of simple and compound events, and understand why their values may differ for a given event in a particular experimental situation.
• Apply statistical concepts and representations to model real world situations.  They will summarize data, make inferences and justify conclusions.
• Use appropriate technology to investigate and represent concepts, methods and application of mathematical concepts.
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems.

MATH 406 - Algebra for Teachers

• Reason using the language and structure of algebra to investigate, represent and solve problems including using algebraic expression, equations, inequalities and systems of equations and inequalities.
• Examine and reason about functional relationships between various representations including graphs, tables, expressions, concrete models and context.
• Analyze, extend and generalize sequences, including arithmetic and geometric sequences, both geometrically and algebraically.  They will write both explicit and recursive definitions for generating a sequence.
• Use and explain the patterns of change in proportional, linear, inversely proportional, quadratic and exponential functions and the types of real-world relationships these functions can model.
• Use appropriate technology to investigate and represent concepts, methods and application of mathematical concepts.
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems.

MATH 407 - Mathematics Honors Seminar - Upper-level

• Name major results in a new field of mathematics.
• Locate and read modern literature in research mathematics.
• Attempt to solve open problems in mathematics.

MATH 410A - Advanced Statistical Methods I

• Evaluate theoretical properties of generalized linear models, including underlying model assumptions and model construction.
• Choose an appropriate generalized linear model, including appropriate choices of distribution, link function, transformations, and interactions.
• Estimate generalized linear models.
• Evaluate the appropriateness and fit of a statistical model, particularly generalized linear models, and interpret the model in context.
• Estimate ANOVA models, and interpret the results.
• Propose a major statistical project, choosing appropriate questions to be answered and appropriate statistical tools.
• Communicate statistical results clearly orally and in writing.

MATH 410B - Advanced Statistical Methods II

• Choose an appropriate regression-based time series model for a data set.
• Evaluate the fit of a time series model and interpret predicted values and prediction and confidence intervals.
• Evaluate the results of a principal components analysis.
• Choose an appropriate decision tree model.
• Choose between various methods of cluster analysis, including K-means and hierarchical clustering, and justify a choice for the number of clusters.
• Conduct a major statistical project, choosing appropriate statistical tools and evaluating the models appropriately.
• Communicate statistical results clearly orally and in writing.

MATH 411A - Probability Theory

• Solve problems involving basic combinatorics.
• Use the axioms of probability.
• Compute conditional probabilities and use them to examine independence of events.
• Describe and use discrete and continuous random variables and their distributions, including multivariate and marginal and conditional distributions.
• Compute and use expectations of random variables, moments, moment generating functions, and conditional expectations.

MATH 411B - Mathematical Statistics I

• Use different discrete and continuous distributions.
• Compute distributions of transformations of random variables.
• Use standard sampling distributions.
• Apply properties of point estimators.

MATH 411C - Mathematical Statistics II

• Find maximum likelihood and method of moments estimators.
• Use interval estimation to answer questions about populations.
• Test hypotheses about a statistical population.

MATH 414 - Time Series Analysis

• Estimate ARMA and ARIMA models for time series data.
• Evaluate the fit of time series models, and choose appropriate models for a given data set.
• Assess time series data for trends and seasonality, and estimate models including these terms.
• Evaluate properties of a time series model given in mathematical form, including checking stationarity and computing the autocorrelation function of a given model.
• Communicate statistical information professionally in writing.

MATH 416A - Actuarial Science Problems II

• Solve problems involving probabilities, conditional probabilities, and continuous and discrete random variables.
• Summarize common families of discrete and continuous probability distributions.
• Apply terminology from insurance to probability questions.
• Choose appropriate tools from probability to solve problems similar to those on the actuarial Exam P.

MATH 416B - Actuarial Science Problems III

• Use the important definitions and theorems in the area of financial mathematics to solve SOA/CAS- style examination problems.
• Answer and solve examination problems accurately and efficiently.
• Communicate their solutions to problems in written and oral form.
   

MATH 417A - Short-Term Actuarial Mathematics I

• Apply techniques for creating a new family of distributions in severity models (including multiplication by a constant, raising to a power, exponentiation, and mixing).
• Compare and contrast various frequency models, including Poisson, Mixed Poisson, Binomial, Negative Binomial, Geometric, and mixture models.
• Solve for relevant parameters and statistics in collective (aggregate) risk models.
• Evaluate the impact of coverage modifications (including deductibles, limits, and coinsurance) in frequency, severity, and aggregate models.
• Evaluate projects using risk measures.
• Design an appropriate actuarial model for a given situation or application.
• Assess the appropriateness of an actuarial model for a given application.

MATH 417B - Short-Term Actuarial Mathematics II

• Estimate parameters for severity, frequency, and aggregate distributions using Maximum Likelihood Estimation.
• Estimate parameters for severity, frequency, and aggregate distributions using Bayesian Estimation
• Choose an appropriate model, using both hypothesis tests and score-based approaches.
• Estimate losses using classical and Bayesian credibility.
• Design an appropriate actuarial model for a given situation or application.
• Assess the appropriateness of an actuarial model for a given application.

MATH 417C - Short-Term Actuarial Mathematics III

• Compare and contrast different types of short-term insurance and forms of reinsurance.
• Compare and contrast the different forms of experience rating.
• Estimate unpaid losses for short-term insurance.
• Evaluate premiums using pure premium and loss ratio methods.
• Design an appropriate actuarial model for a given situation or application.
• Assess the appropriateness of an actuarial model for a given application.

MATH 418A - Financial Mathematics I

• Compare methods of measuring interest and discount, including effective rates, nominal rates, and variable force of interest.
• Value an investment or series of cash flows using variable force of interest.
• Value annuities-certain as of a given date, including level and variable (arithmetic and geometric) annuities and perpetuities.
• Value the outstanding balance, principal paid, and interest paid for a loan at any point in time, including loans with variable interest rates or non-level payments.
• Choose appropriate interest rates for a given problem and justify that choice.
• Communicate financial mathematics results clearly in writing.

MATH 418B - Financial Mathematics II

• Calculate the price, book value, accumulation of discount/amortization of premium, redemption value, coupon rate, or yield rate of a bond given sufficient partial information.
• Estimate the value of an investment using duration and convexity.
• Construct an asset portfolio for Redington immunization, full immunization, and exact matching of a series of liability cash flows.
• Summarize the determinants of interest rates and the components of interest.
• Measure the sensitivity of a valuation to changes in parameters by conducting sensitivity testing.
• Communicate financial mathematics results clearly in writing.

MATH 418C - Financial Mathematics III

• Measure the required return on an asset using capital asset pricing models and factor models.
• Assess a company’s level of risk using different measures of risk and different methods of risk analysis.
• Construct option portfolios to hedge a given position.
• Value options using the Black-Scholes and binomial pricing models.
• Estimate option prices using Greeks, and delta-gamma hedge a portfolio.
• Communicate financial mathematics clearly in writing.

MATH 419A - Long-Term Actuarial Mathematics I

• Compare and contrast long-term coverages in insurance (life, health, general) and retirement benefits (pensions, retiree health care).
• Estimate survival models using nonparametric methods.
• Formulate Markov chain survival models.
• Estimate model quantities using approximations for fractional ages.
• Design an appropriate actuarial model for a given situation or application.
• Assess the appropriateness of an actuarial model for a given application.

MATH 419B - Long-Term Actuarial Mathematics II

• Evaluate and interpret probabilities, means, variance, and percentiles for survival models.
• Estimate the model quantities above using approximation methods.
• Value premiums based on the equivalence principal, the portfolio percentile premium principle, and profit testing.
• Assess the effect on premiums of changes in benefits and underlying assumptions.
• Design an appropriate actuarial model for a given situation or application.
• Assess the appropriateness of an actuarial model for a given application.

MATH 419C - Long-Term Actuarial Mathematics III

• Value net premium reserves, modified reserves, gross premium reserves, and expense reserves.
• Compare and contrast common profit measures.
• Evaluate actuarial accrued liability and normal cost for retirement plans.
• Evaluate the expected present value of future benefits, the accumulated postretirement benefit obligation, and normal cost or service cost for retiree health care plans.
• Assess the impact of changes in underlying valuation assumptions on pension and retiree health care plans.
• Design an appropriate actuarial model for a given situation or application.
• Assess the appropriateness of an actuarial model for a given application.

MATH 430 - Introduction to Theory of Numbers

MATH 440 - Mathematical Theory of Financial Economics

• Become familiar with notations and terminology used in derivatives markets
• Can comprehend and construct interate rate models
• Become familiar with techniques for risk management
• Be capable of rational valuation of derivative securities
• Can comprehend and construct bond price models

MATH 451 - Topology I

MATH 452 - Topology II

• classify topological spaces by topological invariants (e.g., the fundamental group, the Euler characteristic, the knot nolvnomials)
• tell in their own words how to apply these concepts to familiar situations (e.g., spheres, tori, trefoils)
• work cooperatively in the context of mathematics

MATH 453 - Topology III

• Classify topological spaces using topological invariants (e.g., fundamental group, homology group, Euler characteristic, knot polynomials)
• Prove results about classes of topological spaces based on the topological properties of the spaces
• Tie abstract topological concepts to concrete examples of topological spaces found in analysis.
• Determine whether certain topological properties are necessary or sufficient for other topological properties

MATH 455 - College Geometry II

• Utilize inductive and deductive reasoning in the development of geometric notions.
• Utilize the concepts of Neutral geometries to compare all incident geometries
• Utilize the concepts of non-Euclidean geometry in its coordinate free form.
• Utilize the concepts of non-Euclidean geometry in its coordinate form.
• Utilize the concepts of non-Euclidean transformations and their respective invariants in heuristic, coordinate free, and coordinated forms.
• Utilize the concepts of equivalence relations and equivalence classes to identify similar geometric objects.
• Utilize technology appropriately to examine, explore, expand, and explain the concepts of Euclidean Geometry.

MATH 456 - Geometry for Teachers

• Demonstrate an understanding of the axiomatic structure of geometry, including definitions, axioms and theorems and will reason using the language and structure of geometry, both orally and in writing.
• Make conjectures based on inductive reasoning and justify and prove those conjectures using deductive reasoning based on the axiomatic structure of Euclidean geometry.
• Establish congruence and similarity criteria and use them to prove congruence and similarity of polygonal figures.  Students will recognize and use proportional relationships within similar figures to solve problems.
• Investigate the connections between the traditional approach to geometry and a modern approach using transformational geometry.  Students will perform reflection, rotation, translation and dilation in the plane using traditional construction tools as well as using analytic formulas requiring the use of coordinate geometry and matrix and vector operations.
• Use appropriate dynamical geometry software to investigate and represent concepts, methods and application of geometry.
• Use principles of mathematical thinking and problem solving to explore, solve, generalize and prove mathematical problems.

MATH 461 - Abstract Algebra I

• Analyze a given algebraic structure to determine if it satisfies an axiomatic system.
• Write correct proofs within an algebraic axiomatic system.
• Choose necessary and/or sufficient conditions guaranteeing the truthfulness of mathematical statements.
• Assess a problem to determine which theorems to combine to write a correct proof.

MATH 462 - Abstract Algebra II

• Analyze a given algebraic structure to determine if it satisfies an axiomatic system.
• Write correct proofs within an algebraic axiomatic system.
• Choose necessary and/or sufficient conditions guaranteeing the truthfulness of mathematical statements.
• Assess a problem to determine which theorems to combine to write a correct proof.
   

MATH 471 - Advanced Analysis I

• Deduce the behavior of functions by using consequences of uniform convergence.
• Formulate necessary and/or sufficient conditions to guarantee integrability or differentiability of functions.
• Write correct proofs involving uniform convergence, derivatives and integrals.
• Estimate quantities using the triangle inequality in normed spaces as well as the Cauchy- Schwarz inequality.

MATH 472 - Advanced Analysis II

• Deduce the behavior of functions by using consequences of uniform convergence.
• Formulate necessary and/or sufficient conditions to guarantee integrability or differentiability of functions.
• Write correct proofs involving uniform convergence, derivatives and integrals.
• Estimate quantities using the triangle inequality in normed spaces as well as the Cauchy- Schwarz inequality.
   

MATH 473 - Advanced Analysis III

• Write correct proofs.
• Work with limits based on the traditional definition.
• Work with sequences and series using the traditional definition.
• Describe the topology of the real numbers using the terminology of open sets.
• Describe and use properties of sets in the real numbers.
• Define the concept of continuity and apply it to functions.

MATH 475 - Mathematical Modeling

• Select mathematical models to best describe the process of mathematical modeling.
• predict modeling results.
• Assess mathematical models by obtaining numerical results.
• Appraise the requirements of a problem to make modeling decisions, they will judge what to include and what to leave out of a model, and they will defend their choices based on results and constraints.  Students will evaluate which mathematical model performs best in a modeling situation

MATH 476 - Numerical Methods and Analysis I

• Describe, present and analyze numerical methods for a specific data set, and justify their conclusions.
• Construct and analyze computational approximations for different data sets using interpolation and other polynomial approximations.
• Estimate numerical derivatives and numerical integrals for a given dataset.
• Predict and analyze the error propagation that results from mathematical algorithms.
• Evaluate other numerical approximation methods.

MATH 477 - Numerical Methods and Analysis II

• Describe, present and analyze numerical methods for a specific data set, and justify their conclusions.
• Construct and analyze computational approximations for different data sets using interpolation and other polynomial approximations.
• Estimate numerical derivatives and numerical integrals for a given dataset.
• Predict and analyze the error propagation that results from mathematical algorithms.
• Evaluate other numerical approximation methods.

MATH 486 - Mathematical Modeling for Middle-level Teaching

• Connect math concepts and procedures through math modeling for the following math domains: Number & Quantity, Algebra & Functions, Geometry & Measurement, Statistics & Probability, Ratios & Proportional Relationships, and Calculus.
• Plan and teach math tasks for the following math domains Number & Quantity, Algebra & Functions, Geometry & Measurement, Statistics & Probability, Measurement, Ratios & Proportional Relationships, and Modeling.
• Apply and explain the historical and cultural development of each branch of mathematics to the discovery of important mathematics ideas. Use history to plan, teach, and assess students understanding of mathematical concepts.
• Use appropriate technology to investigate and represent concepts, methods, and applications of mathematic problems. Use appropriate technology to teach and assess the mathematical concepts.
• Use mathematical thinking (Mathematical Practices) to solve mathematical problems and justify their solutions.  Plan, teach, and assess lessons involving mathematical thinking using their understanding mathematics learning theory, and pedagogy.
• Use principles of making mathematical connections to create lessons that will engage a diverse student’s population.

MATH 489A - Actuarial Senior Seminar: Predictive Analytics and Actuarial Modeling

• Assess the strengths and weakness of data and conduct basic data validation
• Formulate an actuarial problem in terms that are amenable to a solution.
• Select an appropriate model that addresses an actuarial problem.
• Evaluate a model and assess whether the model is valid for its intended purpose.
• Communicate the results of an actuarial analysis clearly, including any limitations and uncertainties.

MATH 490 - Cooperative Education

MATH 491 - Workshop

MATH 495 - Undergraduate Research

MATH 496 - Individual Study

MATH 497 - Honors

MATH 498 - Special Topics

MATH 499 - Seminar

MATH 499A - Senior Seminar: Actuarial Science

MATH 499E - Senior Seminar: Secondary Mathematics

MATH 499S - Senior Seminar