Math 210: Linear Algebra

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1 Math 210: Linear Algebra MWF 8:30-9:40, Ivers 225 Concordia College, Spring 2009 Dr. Anders Hendrickson Ivers 234G Textbook: Linear Algebra: Gateway to Mathematics, by Robert Messer, supplemented with handouts Course website: Office Hours: Monday 2:40 4:00, Thursday 8:00 9:30, or by appointment. me or catch me after class to set up a time to meet. Catalog Description and Prerequisite: Vectors, matrix algebra, systems of linear equations, determinants, vector spaces, span and basis, eigenvalues and eigenvectors. Also includes an introduction to proof. Prerequisite: Mathematics 122 or consent of the instructor. Curriculum Goals: Success in this course will help you responsibly engage the world in at least three ways: You will learn applied linear algebra techniques used to understand the world in physics, psychology, chemistry, sociology, biology, politics, economics, business, and elsewhere. Through the course s emphasis on proof-writing you will learn to reason clearly and rigorously and to communicate your thoughts with precision. In your study of abstract vector spaces and your engagement with pure reason (guided by intuition), you will see beauty that many people never see, and you will share in God s own delight. Moreover, those of you wishing to become teachers will satisfy portions of the Minnesota Teacher Licensing Requirements through this course; see page 4 for details. Etiquette: You are expected to treat me and your fellow students with respect. In particular, Silence your cell phone ringers before class starts. Do not read newspapers in class. Do not send or receive text messages while in class. Attendance: You are expected to attend all classes. I will cover material in class that is not covered in the book, and you will be held responsible for that material on exams!

2 Linear Algebra Syllabus - Spring 2009 Page 2 of 5 Academic Integrity (Cheating is Pathetic): All exams, quizzes, and homework assignments are subject to Concordia s policy on academic integrity ( In particular, quizzes and exams are to be completed without any assistance from others. This should not need saying, but cheating will not be tolerated. It is an offense against God, against me, and against your classmates who work honestly. If I find evidence of cheating on a test or homework assignment, you will receive zero points on that assignment. Homework: Homework will be assigned and corrected almost every class period. You may indeed, you are encouraged to cooperate with classmates to complete the homework, but you must write up your own solutions to hand in. You will probably find this class s homework much more difficult than that in your earlier math classes, because almost every assignment will ask you to discover proofs. START EARLY!!! Finding proofs requires thinking about the problem, getting stumped, going for a walk, thinking about vectors and subspaces, eating a snack, trying to visualize the problem in a new way, taking a shower, and suddenly the answer will hit you. The homework assignments will be announced in class and posted on the course website. Homework assignments assigned on Friday are nominally due Monday, but may be turned in by noon on Tuesday for full credit. Quizzes and Exams: Quizzes may be given throughout the semester. There will be three in-class exams, currently scheduled for Wednesday, January 28, Friday, February 20, and Monday, March 30. The final exam will be held on Wednesday, April 29 from 8:30 to 10:30 a.m. Absence on the day of an exam results in a zero score, unless you have made prior arrangements with me. Extra Credit: I offer three principal sources of extra credit in this course. First, on many of the homework assignments I will designate one or more problems as extra credit ( XC ) problems. Second, the department offers a colloquium series every other Tuesday at 2:45 p.m.; you can earn up to 10 extra credit points by attending one of the colloquium talks, and turning in a two-page written report about what you learned at the colloquium. You may earn a limit of 20 extra credit points this way. Third, throughout your textbook you will find Projects (see the table of contents). You may earn extra credit by completing those projects in written form; the amount of extra credit awarded will depend both on the difficulty of the project and on how well you complete it. You may earn up to 30 extra credit points this way. All Projects must be turned in to me by Friday, April 17. Calculators: Calculators are neither required nor allowed for this course. All exams and quizzes will be written in such a way that you will not need a calculator.

3 Linear Algebra Syllabus - Spring 2009 Page 3 of 5 Schedule: Class meets in Ivers 225 every Monday and Wednesday from 8:30 to 9:40 and every Friday from 8:00 to 9:10, with just a few exceptions. Please make note of the following special dates: Monday, January 5 First day of class Wednesday, January 28 Exam 1 Friday, February 20 Exam 2 Monday, February 23 No class Spring break Wednesday, February 25 No class Spring break Friday, February 27 No class Spring break Monday, March 30 Exam 3 Friday, April 10 No class Good Friday Monday, April 13 No class Easter Monday Monday, April 27 Last day of class Wednesday, April 29 Final exam, 8:30 10:30 a.m. Grading scale: Grades will be computed according to the scale below. Participation Quizzes & Homework Exam 1 Exam 2 Exam 3 Final Exam Total 50 points 150 points 200 points 700 points (93-100%) A (90-92%) A (87-89%) B (83-86%) B (80-82%) B (77-79%) C (73-76%) C (70-72%) C (67-69%) D (63-66%) D (60-62%) D (0-59%) F

4 Linear Algebra Syllabus - Spring 2009 Page 4 of 5 Minnesota Teacher Licensing Requirements Objective Subpart 3A. A teacher of mathematics understands patterns, relations, functions, algebra, and basic concepts underlying calculus from both concrete and abstract perspectives and is able to apply this understanding to represent and solve real world problems. The teacher of mathematics must demonstrate knowledge of the following mathematical concepts and procedures and the connections among them: (2) analyze the interaction between quantities and variables to model patterns of change and use appropriate representations including tables, graphs, matrices, words, ordered pairs, algebraic expressions, algebraic equations, and verbal descriptions; (7) apply concepts and standard mathematical representations from differential, integral and multivariate calculus; linear algebra, including vectors and vector spaces; and transformational operations to solve problems; Subpart 3B. A teacher of mathematics understands the discrete processes from both concrete and abstract perspectives and is able to identify real world applications; the differences between the mathematics of continuous and discrete phenomena; and the relationships involved when discrete models or processes are used to investigate continuous phenomena. The teacher of mathematics must demonstrate knowledge of the following mathematical concepts and procedures and the connections among them: (6) matrices as a mathematical system and matrices and matrix operations as tools to record information and find solutions of systems of equations; When covered Matrices are used throughout the course; words are used in applications in sections 2.4, 5.3, and 5.4, as well as in proofs written and studied throughout the course; algebraic expressions and equations are used throughout the course. Linear algebra is the subject of the entire course; vectors and vector spaces are covered in Chapters 1, 3, 4, and 6; transformations are covered in Chapter 6. Matrices as a mathematical system are covered in Chapters 5 and 7; various applications discuss using matrices to record information, solutions of systems of equations is covered in Chapter 5.1.

5 Linear Algebra Syllabus - Spring 2009 Page 5 of 5 Objective Subpart 3D. A teacher of mathematics understands geometry and measurement from both abstract and concrete perspectives and is able to identify real world applications and to use geometric learning tools and models, including geoboards, compass and straight edge, rules and protractor, patty paper, reflection tools, spheres, and platonic solids. The teacher of mathematics must demonstrate knowledge of the following mathematical concepts and procedures and the connections among them: (12) three-dimensional geometry and its generalization to other dimensions; (14) extend informal argument to include more rigorous proofs; Subpart 3G. A teacher of mathematics is able to reason mathematically, solve problems mathematically, and communicate in mathematics effectively at different levels of formality and knows the connections among mathematical concepts and procedures as well as their application to the real world. The teacher of mathematics must be able to: (1) solve problems in mathematics by: (b) solving problems using different strategies, verifying and interpreting results, and generalizing the solution; (c) using problem solving approaches to investigate and understand mathematics; (4) make mathematical connections by: (d) making connections between equivalent representations of the same concept. When covered Generalize R 2 and R 3 to R n in the context of vectors ( 1.5). As this is the gateway course for the major, proof writing is covered throughout the course, with an introduction to proof writing techniques given in Chapter 1. This is addressed in sections and 5.2 by solving systems of equations by either substitution, the Gauss-Jordan method, or matrix inverses. This is addressed when writing and studying proofs throughout the course as well as when discussing applications (sections 2.4, 5.3, 5.4). Addressed in solving systems of linear equations through substitution, elimination and the Gauss-Jordan method; also addressed in the concept of isomorphic vector spaces

Course Syllabus for Math

Course Syllabus for Math 1090-003 Instructor: Stefano Filipazzi Class Time: Mondays, Wednesdays and Fridays, 9.40 a.m. - 10.30 a.m. Class Place: LCB 225 Office hours: Wednesdays, 2.00 p.m. - 3.00 p.m.,