MA 405. Introduction to Linear Algebra and Matrices Lecture details Section 001 MWF 9:35-10:25 SAS 2225 Instructor: Anila Yadavalli SAS 3213 ayadava@ncsu.edu https://anilayadavalli.wordpress.ncsu.edu/ Office Hours: M. 10:30-11:30AM, Th. 10:00-11:00AM, and by appointment Moodle page: http://moodle.wolfware.ncsu.edu/ Course text Linear Algebra Done Right, by Sheldon Axler, Springer International Publishing : Imprint: Springer, 2015 ISBN: 9783319110806 - available through NCSU libraries. Helpful (but not required) texts Linear Algebra and its Applications, by David C. Lay, Pearson Education International, any edition ISBN: 0321149920 Introduction to Linear Algbera with Applications, by Jim DeFranza and Daniel Gagliardi, Waveland Press, Inc. ISBN: 1478627077 Course overview Prerequisite: MA 241 (Co-requisite MA 242) Linear Algebra provides one of the cornerstones for much of modern Mathematics, and has important applications in Physics, Engineering, and Economics. The main purpose of this course is to introduce the basic concepts from linear algebra, explain the underlying theory, the computational techniques, and study how these concepts and results can be productively used in other areas of mathematics and physical sciences, especially in applied mathematics where multivariable models are involved. Among the topics covered in this course will be: solving systems of linear equations using Gauss elimination, row echelon form, determinants, vector spaces, linear independence, bases, dimension, linear transformations, orthogonality, eigenvalues, and reduction of matrices to diagonal forms. The subject involves a mixture of both the practical and the theoretical, and will provide in particular a good introduction to mathematical proofs. For this reason, the course is considered to be a difficult one in undergraduate mathematics, and the student should be prepared to invest considerable amount of time in understanding the class material and doing homework. Credit is not allowed for both MA 305 and MA 405. Learning Objectives Upon successful completion of this course, students will be able to: 1. Use Mathematical Notation and Terminology. 2. Understand and Communicate the Fundamental Concepts of Linear Algebra. 3. Identify and Utilize Linear Algebra Tools. 4. Develop Cognitive Skills. Grading Policy The grading will be assigned on a 10-point scale: A+ 99 A 98.9-93 A- 92.9-90 B+ 89.9-87 B 86.9-83 B- 82.9-80 C+ 79.99-77 C 76.9-73 C- 72.9-70 D+ 69.9-67 D 66.9-63 D- 62.9-60 F < 60
Your final grade in this course will be determined as follows: Homework = 30 % Three midterms = 42 % Final Exam = 21 % Classroom Participation = 7 % Three Exams 42% There will be three closed book, in-class tests on February 2, March 2, and April 13. Final Exam 21% The final exam is mandatory, cumulative and will be held in the usual classroom on Monday, April 30, 2017, 8:00-11:00AM. Homework Assignments 30% Homework will be assigned and collected approximately every two weeks. The homework assignments will be available on Moodle. Homework should be written up neatly or typed in LaTeX. All solutions must be completely justified. Students are encouraged to collaborate on homework as long as everyone in the group gains a thorough understanding of the solution. Each student must write up the solution in their own words based on their own understanding, keeping academic integrity in mind. Please list the names of everyone you have collaborated with at the top of your assignment when you turn it in. Additional problems will be available through WeBWorK, but will not count for a grade. It is in your best interest to complete these optional problems as they are fair game for exams. Participation/Presentations 7% This course will rely heavily on classroom collaboration and participation. Students will have many opportunities to present problems at the board or in small groups. Everyone must present at least one problem during the semester. Students will be expected to engage actively, respectfully, and inclusively with their classmates during and outside of class. Group activities are not a time to relax, chit-chat, or let someone else do all the work. Corrections to the grading If you believe an error has been made in grading, please write a statement making your case and bring it to your instructor within 24 hours. Do not alter the original work! Test Make-Up Policy If you miss an exam for undocumented reasons, you will receive a zero. All anticipated absences must be excused prior to the test date. These include university duties or trips (certified by an appropriate faculty or staff member), required court attendance (certified by the Clerk of Court), military duty (certified by the student s commanding officer), or religious observances (certified by the Department of Parent and Family Services 515-2441). Emergency absences must be reported as soon as possible once returning to class and must be appropriately documented (illness by an attending physician or family emergencies by Parent and Family Services). If you are sick on a test day and decide not to come to class, go to the health center or other medical facility. Students who miss a test and have a university-approved excuse must submit appropriate documentation. Attendance Poor attendance serves as its own penalty because material takes much longer to learn independently. You are responsible for keeping up with missed work so that you do not fall behind. Office hours will not be utilized to re-teach material presented in class. Poor attendance may negatively impact your participation grade. Students with disabilities Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State s policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1) Please schedule all DSO exams at least two days prior to the first exam.
Academic Integrity Statement and Academic Dishonesty Academic dishonesty is the giving, taking, or presenting of information or material by a student that unethically or fraudulently aids oneself or another on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student s record or academic career. (NCSU Code of Student Conduct) All students are expected to comply with the University policy on academic integrity. Any suspected violations will be reported. Adverse Weather Announcements regarding scheduled delays or the closing of the University due to adverse weather conditions will be broadcast on local radio and television stations and posted on the University homepage. Non-Discrimination Policy NC State University promotes equal opportunity and prohibits discrimination and harassment based upon one s age, color, disability, gender identity, genetic information, national origin, race, religion, sex (including pregnancy), sexual orientation and veteran status. (NCSU Non-Discrimination Policy) In my classroom, diversity and individual differences are respected, appreciated, and recognized as a source of strength. Students in this class are encouraged and expected to speak up and participate during class, and to carefully and respectfully listen to each other. Every member of this class must show respect for every other member of this class, so that everyone feels comfortable participating. Any attitude or belief that implies that one person or group of people is superior to another is not welcome. Such beliefs are destructive to our classroom community and will hinder our ability to learn from each other. Instructor s commitment You can expect your instructor to be courteous, punctual, well organized, and prepared for lecture and other class activities; to answer questions clearly and in a non-negative fashion; to be available during office hours or to notify you beforehand if they are unable to keep them; to provide a suitable guest lecturer when they are traveling; and to grade uniformly and consistently according to the posted guidelines. Statement of Encouragement Learning math is like learning a new language, and is best done collaboratively. Please work with your classmates (while keeping academic integrity in mind), and do not get discouraged if you do not understand a topic immediately. There is no such thing as a math brain, nor is mathematical ability innate, so each student should be able to succeed by putting in the necessary effort. Please be aware that everyone in this class will learn and progress at different paces, and you should avoid comparing yourself to others.
Course Policies You do not need an appointment to attend my scheduled office hours. If you cannot attend the scheduled office hours, email me to set up an appointment as opposed to just showing up at my office. You do not need to e-mail me if you are missing class. The best way to contact me is by email. Please make sure that you include your name and the course number in the subject of the e-mail. Do not respond directly to emails that I send to the entire class, as they will get archived and I may not see them. Your email address registered with the NCSU online directory will be used for announcements associated with this class. It is your responsibility to maintain a valid email address and check your inbox regularly. The test grades will be recorded on Moodle. Please notify me immediately if you notice any discrepancies in your grades. Keep all your quizzes and tests for future reference. Please check Moodle regularly, as it will be continuously updated with announcements, any changes in the schedule, homework problems, solutions, review sheets, and other additional course materials. Please mark the test dates on your calendar and do not schedule medical appointments, interviews, personal travel, etc. on the test dates. Be respectful to your peers and to your instructor. The use of cell phones and laptops is not permitted in class unless approved by the instructor. Students who fail to comply may be asked to leave class. If you are registered to take exams at the DSO, please schedule all four exams at least two days before Exam 1.
MA405 Tentative Schedule Week 1. Euclidean Vector Spaces. Vector Spaces. Examples. (1.A, 1.B) Week 2. Subspaces. Span (1.C, 2.A) Week 3. Linear Independence, (2.A) Week 4. Basis & Dimension (2.C) Week 5. Row space/column space/null Space/ Rank Theorem. (Instructor Notes) Week 6. Coordinates. Change of Basis. (Instructor Notes) Week 7. Linear Maps. Kernel, Range or a Linear Map (3.A, 3.B) Week 8. Linear Maps continued (3.B) Week 9. Matrix Theory. Invertible matrices. (3.C) Week 10. Isomorphisms. (3.D) Week 11. Eigenvalues & Eigenvectors (Instructor Notes) Week 12. Eigenspaces. Diagonalization. Similarity (Instructor Notes) Week 13. Inner Product Spaces. Orthonormal Bases. Gramm-Schmidt process. (6.A, 6.B) Week 14. Orthogonal Complements. Least squares approximation. (Instructor Notes) Week 15. Diagonalization of symmetric matrices. Singular Value Decomposition. (Instructor Notes)