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Course Criteria
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3.00 Credits
This course is based on the Basic Cryptography Knowledge Unit as defined by the National Security Administration for institutions of higher education. The intent of this course is to provide students with a basic understanding of cryptography and where and how it is used. This course will involve basic programming. A project is required. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Students will be able to identify the elements of a cryptographic system. 2. Students will be able to describe the differences between symmetric and asymmetric algorithms. 3. Students will be able to determine which cryptographic protocols, tools and techniques are appropriate for a given situation. 4. Students will be able to outline how crypto can be used, strengths and weaknesses, modes, and issues that have to be addressed in an implementation. Prerequisites: MATH 1210 and CS 1400 (Both grade C or higher). SP (even)
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3.00 Credits
This course provides an exploration into the historical development of mathematics. The curriculum aims to trace the evolution of important mathematical concepts from their historical inception to their modern form, interpreted through the lens of various cultures and societies. An integral part of this study is the examination of the roles of power and privilege within the history of mathematics education. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Learn the development of mathematical topics, such as geometry, algebra, and calculus within their historical context focusing on the applications that have driven key discoveries. 2. Investigate the roles and roots of power and privilege in math history and learn to identify potential inequities and promote equitable opportunities. 3. Recognize the value of diversity in culture, language, and thought in the historical development of approaches to mathematics. 4. Learn how to solve mathematics problems in the style of each culture under study. Prerequisite: MATH 1220 (Grade C or higher). FA (odd)
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3.00 Credits
A content course designed for Math Education majors who aspire to teach mathematics at the secondary school level. This course is designed to provide a deeper understanding of the content knowledge needed for teaching algebraic content in middle school and high school mathematics classes and strategies for delivering that content in an equitable, learner-centered environment. Using the historical development of content and perspectives from diverse cultures, this course explores the roles and roots of power and privilege in the history of mathematics education. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Develop a rigorous and comprehensive understanding of the algebraic content in the Utah mathematics core curriculum. 2. Learn strategies for delivering algebraic content, focusing on providing equitable access, support, and challenges in a learner-centered environment. 3. Analyze diverse mathematical approaches to algebraic topics with an eye toward leveraging student funds of knowledge to enhance student progression in mathematical learning. 4. Demonstrate practices and processes for teaching students to make connections to mathematical applications within the context of algebra. 5. Demonstrate proficiency with tools and technology designed to support mathematical reasoning and sense-making within the context of algebra. Prerequisite: MATH 1210 (Grade C or higher). FA (even)
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3.00 Credits
A content course designed for Math Education majors who aspire to teach mathematics at the secondary school level. This course is designed to provide a deeper understanding of the content knowledge needed for teaching geometric and statistical content in middle school and high school mathematics classes and strategies for delivering that content in an equitable, learner-centered environment. Using the historical development of content and perspectives from diverse cultures, this course explores the roles and roots of power and privilege in the history of mathematics education. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Develop a rigorous and comprehensive understanding of the geometric and statistical content in the Utah mathematics core curriculum. 2. Learn strategies for delivering geometric and statistical content, focusing on providing equitable access, support, and challenges in a learner-centered environment. 3. Analyze diverse mathematical approaches to geometric and statistical topics with an eye toward leveraging student funds of knowledge to enhance student progression in mathematical learning. 4. Demonstrate practices and processes for teaching students to make connections to mathematical applications within the contexts of geometry and statistics. 5. Demonstrate proficiency with tools and technology designed to support mathematical reasoning and sense-making within the contexts of geometry and statistics. Prerequisite: Math 1210 (Grade C or higher). FA (odd)
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3.00 Credits
The purpose of this course is to equip students with basic theoretical and practical knowledge of stochastic modeling, which is very important and necessary for the analysis of stochastic dynamical systems in many application including economics, engineering, and other other fields. Emphasis will be placed on understanding the stochastic processes, how to model problems, and how to use technology to solve real-world problems. Throughout this course, different real-world problems will be discussed and solved using computational tools. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Explain the basic concepts of stochastic processes. 2. List the different important stochastic processes, their properties and characteristics. 3. Model and solve real-life problems using stochastic processes. Prerequisites: MATH 2050 OR STAT 2040 OR MATH 3060 OR Math 3400 (Grade C or higher). SP
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3.00 Credits
The purpose of this course will be to provide undergraduate students a solid background in the core concepts of applied biological statistics and the use of the software R for data analysis. Specific topics include tools for describing central tendency and variability in data; methods for performing inference on population means and proportions via sample data; statistical hypothesis testing and its application to group comparisons; issues of power and sample size in study designs; and random sample and other study types. While there are some formulae and computational elements to the course, the emphasis is on interpretation and concepts. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Recognize the importance of data collection and its role in determining scope of inference. 2. Demonstrate a solid understanding of interval estimation and hypothesis testing. 3. Choose and apply appropriate statistical methods for analyzing one or two variables. 4. Interpret statistical results correctly, effectively, and in context. 5. Use R to perform descriptive and inferential data analysis for one or two variables. FA, SP
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3.00 Credits
Includes axiomatic development of Euclidean and non-Euclidean geometry. Computer-based GeoGebra program is used. 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. Understand the role of axioms in Euclidean and Non-Euclidean geometry. 2. Proficiently write geometric rigorous proofs. 3. Use technology to explore and conjecture geometric results. Prerequisite: MATH 2200 (Grade C or higher). SP (odd)
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3.00 Credits
An introduction to proofs and the mathematical writing needed for advanced mathematics courses. This course covers logic and methods of mathematical proof in the framework of sets, relations, functions, cardinality, etc. A project is required. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Reformulate statements from common language to formal logic and develop proofs of these statements using common proof methods. 2. Apply the creative process of inventing and discovering new mathematical theories. 3. Apply the methods of thought that mathematicians use in verifying theorems, exploring mathematical truth and developing new mathematical theories for application. 4. Utilize the LaTeX typesetting environment to produce technical and mathematical papers that meet the current formatting standard for circulation within the scientific community. Prerequisites: MATH 2200 or CS 2100 (Grade C or higher); and MATH 1220 (Grade C or higher). FA
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3.00 Credits
First-Order Partial Differential Equations (PDEs), Second-Order PDEs, Fourier Series, The Heat Equation, The Wave Equation, Laplace's Equation, The Fourier Transform Methods for PDEs. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Understand the wave, heat, and Laplace equations and their applications. 2. Utilize Fourier series and the Fourier transform to solve partial differential equations. 3. Understand Sturm-Liouville eigenvalue problems and receive an introduction to solving PDEs numerically. Prerequisite: MATH 2210 and MATH 2270 and MATH 2280 (all Grade C or higher). FA (odd)
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3.00 Credits
This course provides an introduction to the fundamental concepts of mathematical analysis, covering sets and real numbers, sequences and series, basic topology, limits and continuity, the derivative, and sequences and series of functions. The course emphasizes the development of critical thinking and logical reasoning skills, as well as the ability to communicate mathematical ideas effectively through constructing clear, logical proofs. **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Develop a foundational understanding of the key concepts and principles of mathematical analysis for functions of one variable. 2. Appreciate the axiomatic approach to mathematics and application of fundamental principles to build robust mathematical models. 3. Communicate mathematical ideas effectively in writing and speech, emphasizing clear, logical proofs. 4. Apply the techniques of mathematical analysis to solve problems in other areas of mathematics. Prerequisites: MATH 3120 (Grade C or higher); AND MATH 1220 (Grade C or higher). SP
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