MATH MWF 9am Lee, J MATH

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1 Math 2360 Linear Algebra Syllabus and Policies Spring Texas Tech University MATH MWF 9am Lee, J MATH We will use "WebAssign". Introduction to platform given on second class day Linear Algebra (2360) Class hours: MWF 9:00-9:50 AM Class room: MATH.111 Instructor: Jeffrey M. Lee Office: MA 239 Office hours: Regular hours M-F 8:00-8:50 and by appointment ttu.edu Instructor homepage: COURSE DESCRIPTION Linear algebra is the study of systems of linear equations and the related concepts of vector spaces and linear transformation. It is possibly the most important and useful mathematical topic of all. This is especially true in recent years because of the widespread availability of increasingly powerful computers. One can never know too much linear algebra. The class is focused on the solution of concrete problems, but also on abstract ideas and applications to science and engineering.

2 Required text: Elementary Linear Algebra, 8 th edition by Ron Larson, Cengage. Note: The text will be heavily supplemented with other resources supplied to the student including what is presented in class. Material not found in the text will be presented. Prerequisites: Math 1352/1452 or consent of the department. Student learning outcomes: Math 2360 satisfies the university s core curriculum requirement in mathematics: Students graduating from Texas Tech University should be able to demonstrate the ability to apply quantitative and logical skills to solve problems. It meets the following TTU general education student learning outcomes for mathematics, that students will: Apply arithmetic, algebraic, geometric, statistical, and logical reasoning to solve problems. Abstract reasoning will be required. Represent and evaluate basic mathematical and/or logical information numerically, graphically, and symbolically. Interpret mathematical and/or logical models such as formulas, graphs, tables, and schematics, and draw inference from them. In the class, the students will develop skills in manipulating matrices and understand their relationship to linear systems of equations. The students will develop an understanding of the concept of vector spaces including bases, linear transformations, eigenvectors, and eigenspaces. Students will learn the fundamental theorem of linear algebra regarding column space and null space for a matrix and its transpose. Students will be encouraged to develop geometrical intuition. Also, specifically, the students will learn to Solve systems of linear equations Perform matrix arithmetic and compute the determinant of a matrix Perform the Gram-Schmidt orthogonalization process. Compute eigenvalues and eigenvectors. Diagonalization. Compute the determinant, transpose, exponential and, where possible, the inverse of a matrix. Recognize vector spaces and determine their bases Compute the matrix representation of a linear transformation with respect to a given basis. Find the least squares solution to inconsistent systems of linear equations. Calculate projection matrices. Relate the idea of linear algebra to at least some problems and theoretical ideas arising in various scientific fields, engineering and related areas of mathematics such as basic linear differential equations and Fourier series. We will try to cover as many of the following topics as possible: Systems of linear equations (Chapter 1 of the text) Row reduction and echelon forms (Chapters 1 and 2 of the text) Matrix operations, including inverses (Chapter 2) Block matrices (page 51 of text)

3 Abstract vector spaces (Chapter 4) Linear dependence and independence (Chapter 4) Subspaces and bases and dimensions (Chapter 4) Inner product spaces, orthogonal transformations (Chapter 5). Orthogonal bases and orthogonal projections (Chapter 4 and 5 roughly) Gram-Schmidt process (Chapter 5) Linear models and least-squares problems (Chapter 5) Determinants and their properties (Chapter 3) Cramer's Rule Eigenvalues and eigenvectors (Chapter 7) Diagonalization of a matrix (Chapter 7) Symmetric matrices (Explained in class) Positive definite matrices (Explained in class) Linear transformations (Chapter 6) Singular Value Decomposition (Explained in class) LEARNING ASSESSMENT Graded assessment is done through homework and exams. Other assessment techniques will also be used; these include direct questioning, problems to be solved in class, and discussions during office hours. Additionally, problems will be assigned for student self-assessment. The homework problems will be assigned out of the textbook and an online test bank; they will be chosen such that they facilitate the students development of skills in manipulating matrices, solving systems of linear equations, and determining bases for vector spaces. Exam problems will be constructed such as to test if the students have acquired the skills and understanding necessary to perform the basic operations of linear algebra including Gaussian row reduction, determination of null space and column space of a matrix etc. More specific information will be given in class before each exam. Exams: In-class exams times to be announced. Please attend class and contact me in case of unavoidable absence if possible. ASSIGNMENTS, GRADES, AND GRADING Two in-class exams are given during the semester as well as several routine quizzes given at the discretion of the instructor. Grading policy: On exams and written homework, partial credit for correct steps will be awarded even if the final answer is wrong. Full credit will be given only if the final answer and all intermediate steps are correct. A correct final answer does not per se guarantee any credit at all. The Point System. The student s final grade for the course will be based on the total number of points accumulated. First Midterm Exam points Second Midterm Exam points Homework and Quizzes points

4 Final Exam points Total points Deadlines and make ups: Late homework is not accepted except under extraordinary and unavoidable circumstances. In-class exams cannot be made up. Examinations missed for legitimate reasons will receive a pro-rated score based on performance on the final exam. Final Letter Grade The final letter grade will be based on the total number of points accumulated which is converted into a percent of total points possible. Initially the instructor will employ the familiar assignment scheme shown below but a so called grading curve is sometimes employed which may take into account how well the student did compared to others in the class as well as to students that the instructor has taught from previous semesters in the same subject % =A 80-89% =B 70-79% =C 60-69% =D < 60% =F GENERAL POLICIES Academic integrity: It is the aim of the faculty of TTU to foster a spirit of complete honesty and a high standard of integrity. Any attempt of students to present as their own any work that they have not honestly performed is regarded by faculty and administration as a serious offense and renders the offenders liable to serious consequences, possibly suspension. The instructor is very serious and proactive on the issue of cheating; be forewarned. Please see more information on-line at Civility in the classroom: You are expected to be courteous to me and your fellow students. This means that your cell-phone should be turned off during the class; you shall not chat with your friends during class, eat meals or snacks, or cause a distraction in any other way. Officially approved trips: Students are allowed to miss class for trips officially sanctioned by TTU. The student must notify the instructor of upcoming trips and present written authorization. Religious holy days: You are allowed to take the time to travel and observe a religious holy day. Prior notice should be given at least one week before the absence. Students with disabilities (ADA accomodations): Any student who, because of a disability, may require special arrangements in order to meet course requirements should contact the instructor as soon as possible to make any necessary arrangements. Students should present appropriate verification from Student Disability Services during the instructor s hours. Please note instructors are not allowed to provide classroom accommodations to a student until appropriate verification from Student Disability Services has been provided. For additional information, you may contact the Student Disability Services

5 office at 335 West Hall or Material of relevance on the internet: Paul s Online Lecture notes: Linear Algebra Video Lectures from MIT:

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in