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Course Criteria
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3.00 Credits
Mathematics- based statistics. Topics include: Concepts in probability, discrete, continuous and bivariate distributions, distributions of functions of random variables, point and interval estimation, tests of hypothesis, and regression. Calculators with statistical functions is required. Required for Utah Level 3 and 4 Math Endorsement. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Describe properties of probability, counting Techniques, conditional probability and Bayes' Theorem. 2. Use Discrete random variables and Discrete distributions like Binomial, Negative binomial and Poisson distributions. 3. Apply continuous random variables and Continuous distributions like Normal, Exponential, Gamma and Chi-square distributions. 4. Organize Bivariate distributions of discrete and continuous type. 5. Interpret Distributions of functions of one, two or several random variables, Moment-Generating functions and central limit theorem. Prerequisites: MATH 1220 (Grade C or higher). FA
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1.00 Credits
Recommend students to take this class at the same semester as Math 3400. Prepare for Exam P/1 by working on sample exam questions. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Demonstrate through testing the ability to take the Actuarial Probability exam (SOA Exam P/CAS Exam1). Prerequisites: MATH 3400 (Grade C or higher, can be concurrently enrolled). FA
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3.00 Credits
Topics include: point estimation, maximum likelihood estimators and their distributions, sufficient statistics, and Bayesian estimation, confidence intervals for means and proportions, distribution-free confidence intervals for percentiles, confidence intervals for regression coefficients, and re-sampling methods, test hypothesis for means and proportions, The Wilcoxon tests, the power of a test, best critical regions and likelihood ratio tests,, standard chi-square tests, analysis of variance including general factorial designs, and some procedures associated with regression, correlation and statistical quality control. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Explain the concepts of point estimations, order statistics, maximum likelihood estimation, regression, sufficient statistics, and Bayesian Estimation. 2. Construct and interpret confidence intervals for means, differences of two means, proportions, and Percentiles. 3. Explain the concepts of statistical hypotheses, power of statistical test and best critical regions. 4. Perform and interpret hypothesis test for means, proportions. 5. Perform and interpret Chi-square Goodness-of-Fit tests, Test for homogeneity, Test for independence of attributes of classification, One-Factor Analysis of Variance and Two-Way Analysis of Variance. Prerequisites: MATH 3400 (Grade C or higher). SP
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3.00 Credits
Includes numerical solutions of nonlinear equations, interpolation and approximation, numerical integration and differentiation, and solutions of linear systems, numerical solutions of ordinary and partial differential equations, using Maple software to implement various algorithms numerically. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Identify issues of round-off error in numerical approximation using computers/technology. 2. Discuss stability of algorithms, rate of convergence, absolute error and relative error. 3. Implement different root finding algorithms. 4. Construct and use Lagrange polynomials for interpolation and approximation of continuous functions. 5. Implement other types of interpolation methods and perform numerical differentiation and integration methods. 6. Numerically solve ordinary differential equations with initial values. Prerequisites: MATH 2270 AND MATH 2280 (Both grade C or higher), OR MATH 2250 (Grade C or higher). FA (even)
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3.00 Credits
This course introduces students to the fundamentals of mathematical modeling and simulation through the formulation, analysis, and testing of mathematical models in a variety of areas. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, supported using appropriate technology, and on effective communication of quantitative concepts and results. Throughout the course, computational tools are used to implement, examine, and validate these models. Offered upon sufficient student demand. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Transform real-world problems into mathematical form (model). 2. Compute solutions, either exact or approximate, to mathematical models. 3. Translate model solutions back to the real-world context. 4. Assess the quality and reliability of mathematical models. 5. Develop logical reasoning, and quantitative skills. 6. Interpret and communicate their analyses in written and oral form. Prerequisites: MATH 1210 (Grade C or higher). FA (odd)
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4.00 Credits
Development of mathematical models arising in various areas of applications including the mathematical sciences, operations research, engineering and the management and life sciences, and their solution using a wide variety of tools. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Assess and articulate what type of modeling techniques are appropriate for a given dynamical system. 2. Construct a mathematical model of a given dynamical system and analyze it. 3. Predict the behavior of a given dynamical system based on the analysis of its mathematical model. 4. Develop facility in interpreting mathematical models and the conclusions based on the models. Prerequisites: MATH 2280 (Grade C or higher). FA (even)
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3.00 Credits
Overview of number theory and its applications, including the integers, factorizations, modular arithmetic, congruencies, Fermat's and Euler's Theorems, diophantine equations, cryptography, and RSA algorithm. Required for Utah Level 4 Math Endorsement. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Define and investigate divisibility, modular arithmetic, primitive roots, and number theoretic functions. 2. Apply number theory to coding and/or cryptography. 3. Use technology to solve number theoretic applications. 4. Produce rigorous proofs in the context of number theory. Prerequisite: MATH 3120 (Grade C or higher). SP (even)
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3.00 Credits
Applied introduction to classical and modern cryptography. Includes a brief review of the required mathematics, including modular arithmetic and matrix algebra (previous knowledge of these topics is not required). Introduces symmetric (private key) and asymmetric (public key) cryptography, focusing on the algorithms, their security, and attacks on them. Also introduces error-correction codes and and current trends and topics in cryptography. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Explain the differences, challenges, and roles of private-key versus public-key cryptography. 2. Employ modular arithmetic and matrix algebra in applications of cryptography and error-correcting codes. 3. Demonstrate understanding of the theory, application, and weaknesses of classical cryptosystems. 4. Simulate classical and modern cryptosystems as well as error-correcting codes. 5. Apply the common methods of attack on cryptosystems to test security. Prerequisites: CS 1400 (Grade C or higher); and MATH 2200 or CS 3310 (Grade C or higher). FA (even)
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3.00 Credits
For students in all Math-related majors. Covers an introduction to algebraic systems including group rings, fields and sets. Required for Utah Level 3 and 4 Math Endorsements. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Use the definition and basic properties of groups, rings, and fields. 2. Analyze and prove examples of subgroups, normal subgroups, and quotient groups. 3. Use the concepts of homomorphism and isomorphism for groups, rings, and fields. 4. Produce rigorous proofs in the context of Abstract Algebra. Prerequisites: MATH 2270 (Grade C or higher) and MATH 3120 (Grade C or higher). FA
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3.00 Credits
The intent of this course is to introduce quantum computing to a broad audience of computer scientists, engineers, mathematicians, and anyone with a general interest with a sufficient background in mathematics. A hands-on approach is taken throughout, and students will utilize freely available quantum computer developer tools to form a basic understanding of ideas. Topics discussed are the mathematical models of superposition, measurement, and entanglement and how these ideas coalesce to make quantum computing possible. Known quantum algorithms will be introduced as will their impact on current cryptosystems. Previous exposure to quantum mechanics is not required. **COURSE LEARNING OUTCOMES (CLOs) At the successful completion of this course, students will be able to: 1. Explain the elementary quantum phenomena that render quantum technologies viable. 2. Contrast classical computing with new quantum computing approaches to problem solving. 3. Outline the potential benefits and key areas of application of quantum technologies and the challenges in attaining them. 4. Simulate basic quantum algorithms in the context of cryptography. Prerequisites: CS 1400 and either MATH 2250 or MATH 2270 (Both grade C or higher). SP (odd)
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