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The Mathematics Major's Handbook

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The Mathematics Major's Handbook The Mathematics Major’s Handbook (updated Spring 2016) Mathematics Faculty and Their Areas of Expertise Jennifer Bowen Abstract Algebra, Nonassociative Rings and Algebras, Jordan Algebras James Hartman Linear Algebra, Magic Matrices, Involutions, (on leave) Statistics, Operator Theory Robert Kelvey Combinatorial and Geometric Group Theory Matthew Moynihan Abstract Algebra, Combinatorics, Permutation Enumeration R. Drew Pasteur Differential Equations, Mathematics in Biology/Medicine, Sports Data Analysis Pamela Pierce Real Analysis, Functions of Generalized Bounded Variation, Convergence of Fourier Series, Undergraduate Mathematics Education, Preparation of Pre-service Teachers John Ramsay Topology, Algebraic Topology, Operations Research OndˇrejZindulka Real Analysis, Fractal geometry, Geometric Measure Theory, Set Theory 1 2 Contents 1 Mission Statement and Learning Goals 5 1.1 Mathematics Department Mission Statement . 5 1.2 Learning Goals for the Mathematics Major . 5 2 Curriculum 8 3 Requirements for the Major 9 3.1 Recommended Timeline for the Mathematics Major . 10 3.2 Requirements for the Double Major . 10 3.3 Requirements for Teaching Licensure in Mathematics . 11 3.4 Requirements for the Minor . 11 4 Off-Campus Study in Mathematics 12 5 Senior Independent Study 13 5.1 Mathematics I.S. Student/Advisor Guidelines . 13 5.2 Project Topics . 13 5.3 Project Submissions . 14 5.3.1 Project Proposal . 14 5.3.2 Project Research . 14 5.3.3 Annotated Bibliography . 14 5.3.4 Thesis Outline . 15 5.3.5 Completed Chapters . 15 5.3.6 Digitial I.S. Document . 15 5.3.7 Poster . 15 5.3.8 Document Submission and oral presentation schedule . 15 6 Independent Study Assessment Guide 21 7 Further Learning Opportunities 23 7.1 At Wooster . 23 7.2 Beyond Wooster . 24 8 Departmental Honors and Prizes 25 9 Mathematics After Wooster 25 List of Figures 1 Map of Department Learning Outcomes to Courses . 6 2 Map of Department Learning Outcomes to Graduate Qualities . 7 List of Tables 1 Recommended classes for double majors or minors in other fields . 9 2 Recommended classes for majors preparing for graduate school . 10 3 Recommended Timeline for the Mathematics Major . 10 3 4 1 Mission Statement and Learning Goals 1.1 Mathematics Department Mission Statement The Mathematics Department’s mission is to provide quality academic programs in mathematics that will allow students to prepare for graduate work and for employment in mathematics-related positions. Students will develop their analytical and problem solving skills while learning about the beauty of mathematics. In addition to providing specific content knowledge in mathematics, the mathematics program will develop the strong communication skills that are necessary in today’s society. We will also strive to provide courses that will serve the needs of other departments and programs within the college. 1.2 Learning Goals for the Mathematics Major The following five goals are what the department expects majors to achieve by the end of their course of studies. 1. Communication (a) Students should be able to read and understand mathematical statements. (b) Students should be able to express mathematical ideas with precision and clarity orally. (c) Students should be able to express mathematical ideas with precision and clarity in writing. 2. Content (a) Students should know the fundamental concepts, definitions, theorems and techniques of calculus. (b) Students should know the fundamental concepts, definitions, theorems and techniques of linear algebra. (c) Students should demonstrate competence in several specific areas of pure mathematics. (d) Students should demonstrate competence in several specific areas of applied mathematics. 3. Problem Solving/Reasoning (a) Students should be able to reason mathematically using graphical, numerical, and symbolic points of view. (b) Students should be able to write sound proofs. (c) Students should be able to use technology appropriately to solve mathematical problems. 4. Connection (a) Students should be able to synthesize material from multiple perspectives. (b) Students should be able to make connections between different areas of mathematics. 5. Independent and Collaborative Learning (a) Students should demonstrate skills in approaching and solving problems independently. (b) Students should demonstrate skills in working together in teams to solve complex problems. 5 Study - Semester Two 452: Senior Independent A A A A A A A A A A A E/A E/A Study - Semester One 451: Senior Independent A A A A A A A A E/A E/A E/A E/A E/A 400: Tutorial A A A A A Complex Variable 336: Functions of a E E E E E E A A A A A 335: Abstract Algebra II E E A A A A A A A A 334: Abstract Algebra I E E E E E E A A A A 333: Real Analysis II E A A A A A A A A A 332: Real Analysis I E E E E E E A A A A A 330: Topology E E E E E E A A A A Statistics II 329: Probability and E E E E E E E A A A A 327: Numerical Analysis E E E E E E E A A A A 319: Special Topics E E A A A A A A A A 279: Problem Seminar I I I I E E E Statistics I 229: Probability and I I E E E E E E A A 227: Operations Research I I I I E E E E E E E E A Modeling 225: Mathematical I I E E E E E E E E A Graph Theory 223: Combinatorics and I I I I E E E A Courses Equations 221: Differential I I I I E E E E 219: Special Topics E E A A I/E Advanced Mathematics 215: Transition to I I I E E E E E 212: Multivariate Calculus I I I I I I E E E E 211: Linear Algebra I I I I E E E Mathematics 123: Discrete I I I I I I Geometry II 112: Calculus and Analytic I I I I I I E Geometry I 111: Calculus and Analytic I I I I I I I Algebra B 108: Calculus with I I I I I I Algebra A 107: Calculus with I I I I I Science 104: Calculus for Social I I I I 6 102: Basic Statistics I I I I I I Contemporary Society 100: Math in I I I Department Learning Outcomes Reading and Understanding Mathematical Statements Clear Oral Expression of Mathematics Clear Mathematical Writing Calculus Competence Linear Algebra Competence Broad Competence Beyond Calculus and Linear Algebra Graphical, Numerical, and Symbolic Reasoning Sound Proof Writing Pertinent Technology Usage Synthesize Material from Multiple Perspectives Make Connections Between Different Areas of Math Independent Problem Solving Collaborative Problem Solving Learning Reasoning Collaborative Communication Content Connection Problem Solving / Independent/ Figure 1: Map of Department Learning Outcomes to Courses community & serving others Exhibit a commitment to for social justice leadership & embody a concern Demonstrate ethical citizenship & beliefs including their own Appreciate and critique values & Responsibility Civic and Social community diverse local, national, and global of their role as citizens in a Display self-reflective awareness cultural & religious traditions Understand and respect diverse a second language community through knowledge of Engage with the global & implications of global processes Understand the histories, causes, Respect for Diversity Global Engagement and questioning, and reasoning through active listening, X X X X X X X X X X X X Engage in effective discourse digital communication Exhibit skill in oral, written, and X X X X X X X X X X Effective Communication X X X X X X X X X X X X X world problems and judgement to solve real X X X X X X X X Employ deep knowledge, insight, Graduate Qualities textual, visual, & digital literacy Demonstrate quantitative, X X X X X X X X X X X X X disciplines methodologies from multiple X X Evaluate evidence using physical and natural sciences social sciences, mathematics, and knowledge in arts, humanities, X X X X X X X X X X X X X Understand disciplinary the Liberal Arts Dynamic Understanding of X X X X X X X X X X X X X collaboration Engage in effective intellectual X X X X practice Actively integrate theory & X X X X X X multiple disciplines Synthesize knowledge from X X 7 Collaborative Inquiry Integrative and X X necessary for life-long learning passion, & self-confidence X X X X X Embody the intellectual curiosity, Creative project bring to fruition a complex and X X X X Devise, formulate, research, and Engage in critical thinking X X X X X X X X X X X X Independent Thinking X X X X X X of Mathematics Reasoning Perspectives Reading and Understanding Mathematical Clear Oral Expression of Mathematics Clear Mathematical Writing Calculus Competence Linear Algebra Competence Broad Competence Beyond Calculus and Graphical, Numerical, and Symbolic Sound Proof Writing Pertinent Technology Usage Synthesize Material from Multiple Make Connections Between Different Areas Independent Problem Solving Collaborative Problem Solving Linear Algebra Statements Department Learning Outcomes Communication Content Problem Solving / Reasoning Connection Independent and Collaborative Learning Figure 2: Map of Department Learning Outcomes to Graduate Qualities 2 Curriculum Core Courses 111. Calculus and Analytic Geometry I (or 108. Calculus with Algebra B) • 112. Calculus and Analytic Geometry II • 211. Linear Algebra • 212. Multivariate Calculus • 215. Transition to Advanced Mathematics [(W) Writing Intensive] • 200-Level Courses 221. Differential Equations • 223. Combinatorics and Graph Theory • 225. Mathematical Modeling • 227. Operations Research • 229. Probability and Statistics I • 299. Special Topics • Problem Solving 279. Fall Problem Seminar preparation for the Putnam Competition • 279. Spring Problem Seminar Exploratory Mathematics or preparation for the Modeling contest • 300-Level Courses 327.
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