Math 321 - Linear Algebra with Proofs, Fall 2021

Time and Location:	Tue 11:00 am - 12:15, Zoom Discussions & Lectures Thur 11:00 am - 12:15, typically in MITCH 220
Office Hours:	Wed 4:10 - 5:00 pm in Zoom; also by email; also ask questions in class; also request other Zoom time in case of conflicts
Professor Info:	Anna Skripka, skripka [at] math [dot] unm [dot] edu

Description: Math 321 is an introductory course in linear algebra geared towards mathematics and physics majors. The course is designed to teach the concepts and techniques of basic linear algebra as a rigorous mathematical subject. Besides computational proficiency, there is an emphasis on understanding definitions and theorems, as well as reading, understanding, and creating proofs. (There is a less abstract linear algebra course - Math 314.) The main topics of the course include linear systems, matrices, determinants, eigenvalues and eigenvectors, diagonalization, vector spaces, norm and inner product spaces, linear transformations, representations.
Expect spending 9-12 hours per week on this course (3 hours of lectures and 6-9 hours of individual/group study). There are many abstract concepts and different types of problems (both computational and theoretical) in this course. It will take a considerable amount of time and effort on your part to fully master them. Unfortunately, due to the time constraint, we will not be able to discuss every type of problems in full details during the lectures.
Course goals and basic study guide are posted on Learn
Prerequisite: Calculus III (required), Math 327 (strongly recommended if you have not had a proof based class before)

Course Resources: zoom link, lecture notes, handouts, goals, assignments, zoom recordings are to be posted on Learn. The completed assignments are to be submitted on Learn; the grades and feedback are to be posted on Learn.
Tutoring: CAPS
Textbook: Jeffrey Holt, "Linear Algebra with Applications", 1st edition, W. H. Freeman, ISBN-10: 0716786672
Supplementary reading:
Sergei Treil, Linear Algebra Done Wrong
R. A. Beezer, A First Course in Linear Algebra
Schaum's Outline of Beginning Linear Algebra, McGraw-Hill, 2018
T. Sundstrom, Mathematical Reasoning: Writing and Proof
Some video lectures on linear algebra: MIT18.06, MIT18.065, JHU, UCI, Essence of LA, KhanAcademy
Some resources on related topics: Communicating in Mathematics/Proof Writing, How To Study Math
Online calculators: Sage/Octave, Octave, Matlab
Free PDF scanners: CamScanner, TinyScanner

Grades: 5% for polls (answers to questions asked during zoom meetings), 35% for homework+quiz, 60% for three exams (two midterm and one final).
Policies: You are expected to attend every classroom meeting and come prepared by reading the book on new material ahead of lectures as well as reading lectures and doing exercises on old material.
The homework is to be submitted on UNMLearn as a single PDF file. Please make sure that the files you submit are legible. Your work will be graded on the clarity, completeness, correctness of your reasoning and presentation. On the homework assignments you are allowed to work in groups, but you must write up your own solutions in your own words. Submitting solutions obtained from third parties, including the internet, is strictly prohibited.
NO LATE ASSIGNMENT WILL BE ACCEPTED, but two lowest scores on homework/quizzes will be dropped to accommodate for unavoidable circumstances such as emergencies, illnesses, official UNM function. (You can start working on the assignment as soon as it is posted without waiting for the day it is due.) A replacement by a final exam score or make-up exam will be given for a missed midterm exam only in case of a documented absence prescribed by the university (family emergency, serious medical problem, official UNM function). All objections to grades should be made within one week since the assignments are graded.

Tentative Schedule (to be updated at the end of each week)

Week	Class dates	Book sections	Topics
1	Aug 24, 26	1.1, 1.2; home reading: 1.3	Systems of linear equations (SLE). Gauss-Jordan Elimination. Theorems on the number of solutions. Applications of SLE.
2	Aug 31, Sep 2	2.1, 2.2	Vectors. Span. Spanning property. Basic logic.
3	Sep 7, 9 Drop with no grade: Sep 10	2.3	Linear Independence. Homogeneous versus non-homogeneous SLE.
4	Sep 14, 16	3.1, 3.2	Linear Transformations. Matrix algebra.
5	Sep 21, 23	3.2, 3.3	Matrix algebra. Inverses.
6	Sep 28, 30	4.1, 4.2	Subspaces. Basis.
7	Oct 5, 7 (Exam 1)	covered material of 1.1 - 3.3	Review.
8	Oct 12	4.3, 4.4	Dimension. Row and column spaces. Change of basis.
9	Oct 19, 21	5.1, 5.2, 5.3	Determinant. Properties and applications of the determinant.
10	Oct 26, 28	6.1, 6.2, 3.5	Eigenvalues and eigenvectors. Diagonalization. Markov chains.
11	Nov 2, 4	8.1, 8.2	Dot product and orthogonality. Projection.
12	Nov 9, 11 Withdrawal deadline: Nov 12	8.2, 8.5	Gram-Schmidt orthogonalization process. Least squares regression.
13	Nov 16, 18 (Exam 2)	covered material of 3.3 - 6.2	Review.
14	Nov 23	8.3, 8.4	Orthogonal diagonalization. Singular value decomposition.
15	Nov 30, Dec 2	7.1, 7.2, 7.3	Abstract vector spaces. Basis. Dimension.
16	Dec 7, 9	10.1, 10.2	Orthogonality. Projection. Review.
17	Dec 14 (Tuesday), 12:30 - 2:30 p.m. Final Exam

Academic Integrity: Each student is expected to maintain the highest standards of honesty and integrity in academic and professional matters. The University reserves the right to take disciplinary action, including dismissal, against any student who is found responsible for academic dishonesty. Any student who has been judged to have engaged in academic dishonesty in course work may receive a reduced or failing grade for the work in question and/or for the course. Academic dishonesty includes, but is not limited to, dishonesty on quizzes, tests or assignments; claiming credit for work not done or done by others (plagiarism); and hindering the academic work of other students.
Copyright Policy: All materials disseminated in class and on the course webpage are protected by copyright laws and are for personal use of students registered in the class. Redistribution or sale of any of these materials is strictly prohibited.
American Disabilities Act: In accordance with University Policy 2310 and the American Disabilities Act (ADA), reasonable academic accommodations may be made for any qualified student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor's attention, as the instructor is not legally permitted to inquire. The student is responsible for demonstrating the need for an academic adjustment by providing Student Services with complete and appropriate current documentation that establishes the disability, and the need for and appropriateness of the requested adjustment(s). However, students with disabilities are still required to adhere to all University policies, including policies concerning conduct and performance. Contact Accessibility Resource Center at 505-277-3506 or arcsrvs@unm.edu for additional information.
UNM Requirement on Masking in Indoor Spaces: All students, staff, and instructors are required to wear face masks in indoor classes, labs, studios and meetings on UNM campuses, see masking requirement. Students who do not wear a mask indoors on UNM campuses can expect to be asked to leave the classroom and to be dropped from a class if failure to wear a mask occurs more than once in that class.
UNM Administrative Mandate on Required Vaccinations: All students, staff, and instructors are required by UNM Administrative Mandate on Required Vaccinations to be fully vaccinated for COVID-19 as soon as possible, but no later than September 30, 2021, and must provide proof of vaccination or of a UNM validated limited exemption or exemption no later than September 30, 2021 to the UNM vaccination verification site. Students seeking medical exemption from the vaccination policy must submit a request to the UNM verification site for review by the UNM Accessibility Resource Center. Students seeking religious exemption from the vaccination policy must submit a request for reasonable accommodation to the UNM verification site for review by the Compliance, Ethics, and Equal Opportunity Office. For further information on the requirement and on limited exemptions and exemptions, see the UNM Administrative Mandate on Required Vaccinations.
Disclaimer: It is your responsibility to know and understand the course policies. The professor reserves the right to change this syllabus. This might become necessary in the current circumstances, when rules that are beyond professor's control change frequently. An up-to-date syllabus is posted on this webpage and on UNMLearn.

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