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Course Criteria
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3.00 Credits
Continuation of MATH 4000. Topics include Sylow Theory for finite groups, Galois Theory, factorization in commutative rings. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Understand and explore advanced topics in group theory, ring theory, and field theory. 2. Demonstrate understanding by applying classical topics such as the Sylow theorems and Galois theory to concrete examples of algebraic structures. 3. Explore the application of abstract algebra to areas such as geometry, public-key cryptography, error-correcting codes, etc. 4. Produce rigorous proofs in the context of abstract algebra. Prerequisite: MATH 4000. 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
Designed for pre-service secondary math teachers or those seeking Utah Level 2, 3, 4 Mathematics Endorsement. Course content includes use of curriculum and research in the 7- 12 grade classroom, development of math pedagogical skills, accommodations for diverse learners, factors of motivation, and professional growth. Technology will include graphing calculators, classroom on-line learning systems, and mathematical instructional software. Required for Utah Level 2, 3, and 4 Math Endorsements. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Understand procedures in Secondary classroom. 2. Demonstrate proficiency in teaching 7-12 mathematics. 3. Demonstrate knowledge of methods of teaching mathematics. 4. Demonstrate knowledge of mathematical learning schema of 7-12 students. Prerequisite: MATH 1210 (Grade C or higher). FA
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3.00 Credits
Advanced numerical linear algebra, optimization, nonlinear systems, topics from approximation theory, quadrature, numerical solutions of differential equations. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Demonstrate an understanding of the concepts of efficiency and stability of algorithms in numerical linear algebra. 2. Understand the importance of matrix factorizations, and know how to construct some key factorizations using elementary transformations. 3. Solve linear systems, least squares problems, and the eigenvalue problems. 4. Appreciate the issues involved in the choice of algorithm for particular problems (sparsity, structure, etc.). 5. Appreciate the basic concepts involved in the efficient implementation of algorithms in a high-level language. Prerequisites: MATH 3500 (Grade C or higher). SP (odd)
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