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Course Criteria
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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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3.00 Credits
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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3.00 Credits
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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3.00 Credits
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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4.00 Credits
This course introduces the essentials of scientific computer programming using appropriate high-level languages to solve problems in engineering and science. Programming topics include problem decomposition, control structures, recursion, arrays and other data structures, file I/O, graphics, code libraries, round-off error in floating point arithmetic. Applications will be drawn from numerical integration and differentiation, root finding, matrix operations, searching and sorting, simulation, and data analysis. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Demonstrate proficiency in basic skills related to using MATLAB/Python in scientific computation setting. 2. Apply programming skills to solving challenging problems that are either purely mathematical or arise from other disciplines. Prerequisites: CS 1400 (Grade C or higher) and MATH 2270 (Grade C or higher). Corequisites: MATH 2280. SP
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3.00 Credits
This course introduces topics of linear algebra needed for advanced applications. Topics included are abstract vector spaces, linear transformations, dual spaces, inner product spaces, orthogonality, bilinear forms, eigenvalues and eigenvectors, generalized eigenvectors, diagonalization, and canonical forms. **COURSE LEARNING OUTCOMES (CLOs) At the successful completion of this course, students will be able to: 1. Demonstrate a thorough understanding of the core concepts and solution techniques of linear algebra. 2. Employ linear algebra in various application areas. 3. Utilize technology and computer algebra systems to aid problem solving. 4. Produce and present work in the form of a course project. Prerequisites: MATH 2270 and MATH 3120 (Both grade C or higher). SP (even)
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3.00 Credits
This course focuses on the theoretical basis and mathematical analysis of financial mathematics. This course prepares actuarial students for exam FM in the Society of Actuaries' series (or Exam 2 for the Casualty Actuarial Society). **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Demonstrate the ability to define and recognize terms regarding time value of money. 2. Solve problem related to time value of money. 3. Define and recognize terms regarding annuity. 4. Solve problem related to loans and bonds. 5. Define and recognize terms regarding immunization. 6. Construct various investment portfolio. 7. Take the Actuarial Financial Mathematics Exam (SOA Exam FM/CAS Exam 2). Prerequisites: MATH 1100 (Grade C or higher) or MATH 1210 (Grade C or higher). SP
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1.00 Credits
Recommend for students to take this class the same semester as MATH 4000. Prepare for Exam FM/2 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 Financial Mathematics Exam (SOA Exam FM/CAS Exam 2) Prerequisites: MATH 4400 (Grade C or higher, can be concurrently enrolled). SP
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3.00 Credits
Required for all Special Education majors. Teacher candidates will learn content appropriate for secondary students, effective practices, and strategies to support secondary students with disabilities as they learn about mathematics. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Identify, plan, and implement learning progressions in mathematics. 2. Identify and implement interventions using a tiered approach. 3. Describe and appropriately plan for social emotional factors related to math learning. 4. Describe and identify effective practices for co-teaching mathematics in the secondary classroom. 5. Demonstrate effective teaching practices in mathematics at the secondary level. Prerequisites: Admission to the Utah Tech University Special Education Program. FA, SP
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3.00 Credits
A teaching methods course designed for Math Education majors who aspire to teach mathematics at the secondary school level. It offers practical strategies and methods for effective mathematics instruction in a high school setting. Students will learn how to plan and deliver lessons, develop curriculum, and create assessments. The focus will be on creating an inclusive and equitable learning environment that encourages student engagement with math and helps students build a positive mathematical identity. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Plan and deliver effective, learner-centered math instruction by considering each students needs and strengths, and developing appropriate tasks. 2. Interpret and implement math curricula and standards in the creation of formative and summative assessments that consider students needs, strengths, and course content. 3. Foster student engagement and the promotion of their mathematical identities by valuing each students unique mathematical, cultural, and linguistic contributions. 4. Create a learning environment that encourages diverse mathematical thinking and leverages students funds of knowledge to guide instruction and cultivate confidence. 5. Construct learning opportunities and use planning and implementation practices that provide equitable access, support, and challenges for every student. Prerequisite: MATH 1210 (Grade C or higher). FA
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