Course Search Results

  • MATH 3500: Numerical Analysis

    3.00 Credits
    Utah Tech University

    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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  • MATH 3605: Introduction to Modeling and Simulation

    3.00 Credits
    Utah Tech University

    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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  • MATH 3700: Mathematical Modeling I

    4.00 Credits
    Utah Tech University

    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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  • MATH 3900: Number Theory

    3.00 Credits
    Utah Tech University

    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 1210; and MATH 2200 or CS 2100 (Grade C or higher). SP (even)
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  • MATH 3905: Cryptography and Codes

    3.00 Credits
    Utah Tech University

    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 2100 (Grade C or higher). FA (even)
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  • MATH 4000: Foundations of Algebra

    3.00 Credits
    Utah Tech University

    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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  • MATH 4005: Quantum Computing and Cryptography

    3.00 Credits
    Utah Tech University

    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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  • MATH 4010: Abstract Algebra II

    3.00 Credits
    Utah Tech University

    Continuation of MATH 4000. This course is a continuation of Abstract Algebra I and focuses on a deeper understanding of algebraic structures. We will continue studying group theory, including group actions and the Sylow Theorems. Additionally, we will delve into ring theory, lattice structures and boolean algebras, and field theory. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Learn advanced group theory topics including group actions and the Sylow theorems, and apply them to the study of algebraic structures. 2. Apply abstract algebra to real-world technologies such as circuits and error-correcting codes. 3. Construct and verify mathematical proofs, particularly those arising in abstract algebra. 4. Demonstrate an understanding of ring theory, including ideals, quotient rings, homomorphisms, isomorphisms, and polynomial rings. 5. Learn about finite fields, algebraic and transcendental extensions, and Galois theory; and explore their applications. ?? Prerequisite: MATH 4000 (Grade C or higher). ?? SP (odd)
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  • MATH 4100: Introduction to Topology

    3.00 Credits
    Utah Tech University

    Overview of elementary point-set topology. Includes topological spaces, compactness, connectedness, metric spaces, and Hausdorff spaces. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Describe concepts of and prove fundamental results in point-set topology as needed for advanced work in the mathematical sciences. 2. Develop the ideas of a topology, basis, the Hausdorff property, connectedness, continuous mappings, compactness, and related concepts. 3. Create new topological spaces using the product topology, subspace topology, and quotient topology. 4. Produce rigorous proofs in the context of topology. Prerequisites: MATH 2210 and MATH 3120 (Grade C or higher). FA (odd)
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  • MATH 4200: Introduction to Complex Analysis

    3.00 Credits
    Utah Tech University

    Overview of basic theory and applications of complex variables, including analytic functions, contour integration, and conformal mappings. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Understand arithmetic, algebraic, geometric properties of complex numbers and basic complex functions (mappings). 2. Understand calculus concepts like limit, continuity, and derivatives of elementary complex analytic functions in particular with complex exponential, logarithmic, power, trigonometric, hyperbolic, inverse trigonometric, and inverse hyperbolic functions. Understand how those functions act as mappings of the complex plane. 3. Define integral of complex functions (contour integral). Understand the properties of contour integral and method of evaluation in the complex plane. 4. Understand complex sequences and series including power series, Taylor series, and Laurent series; Implement basic convergent/divergent tests. Understand residual theorem, Laplace transformation, and Fourier Transformation. 5. Understand and utilize conformal mapping to solve boundary-value problems in heat flow, electrostatics, and fluid flow. Prerequisite: MATH 3200.?? ?? SP (even)
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