Math 321 - Linear Algebra

Section: 1 Time: MWF 11:00 - 11:50 a.m. Room: SMLC 120 Syllabus
 
Instructor Info: Anna Skripka, skripka [at] math [dot] unm [dot] edu
Office hours: MWF 3:00 - 3:50 pm and also by appointment, in SMLC 212
 
Textbook: Jeffrey Holt, "Linear Algebra with Applications", 1st edition, W. H. Freeman, ISBN-10: 0716786672
Supplementary reading: Sergei Treil, "Linear Algebra Done Wrong", full text
 
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.
Sample Math 321 goals (might get slightly modified),   Study guide

Video lectures on linear algebra: KhanAcademy, MIT
 
Prerequisite: Math 264 (required), Math 327 (recommended)
Attendance: Students with excessive absences will be dropped from the course according to the university attendance rules. This also applies to the students in the wait list.
Want a regrade? If it is less than a week since the assignments were distributed in class, check the solution key and state precisely in your claim which step of your solution seems to have been overlooked by the grader.
 
Tentative Schedule (will be updated at the end of each week)
 
Week
Class Dates
Book Sections
Topics
Homework
Important Dates, Solutions
1
Jan 22, 24
1.1
Linear systems of equations.
1.1: #7(a,b),19,20,21,23,24,27,28,51,53,54,57,58,60,61
1.2: #11,13,21,22,23,24,25,43,45,46,47,49,50 (submit even #)
Pretest on Jan 22
2
Jan 27, 29, 31
1.2
Elementary row operations. Solving systems. Basic logic, I.
Application 1: photosynthesis.
1.1: #35,37; 1.2:#53,55
for grade, submit the following --> HW2
Q1, HW1 (1.1, 1.2) on Jan 31
3
Feb 3, 5, 7
2.1, 2.2, 2.3
Vectors. Span. Connection to systems of equations. Basic logic, II.
2.1: #11,13,15,17,25,27;  2.2: #11,15,17,25,27, 41--65(odd)
for grade, submit the following --> HW3
Q2, HW2 (over the first 2 weeks) on Feb 7;
Drop without a grade: Feb 7
4
Feb 10, 12, 14
2.3, 3.1
Linear independence. Linear transformations. Basic logic, III.
Application 2: pharmaceutics.
2.3: #3,5,9,15,21,23,27,29, 33-53(odd), 59-65(odd), proofs of Theorems 2.16 and 2.17
3.1: #3,5,7,9,13,15, 19-31(odd), 39,41,43,47,49,55,58,59,61
for grade: 2.2: #58,64; 2.3: #42,48,50; 3.1: #6,14,16,50(c)
HW3 due Feb 14
5
Feb 17, 19, 21
3.1, 3.2
Linear transformations. Matrix algebra.
Application 3: expenses calculation.
3.2: #1,3,9,13(a,b),15,23,25(a,b), 39-45(odd),51,53,55
Q3, HW4 (2.2, 2.3, 3.1) on Feb 21
6
Feb 24, 26, 28
3.2, 3.3
Matrix algebra. Inverses.
3.3: #1-13(odd),21,23,25,27(a),31,35,41,43,47-53(odd),57,59,67
for grade: 3.2: #14(b), 3.3: #22,26,52,56
Exam1 (1.1, 1.2, 1.3, 2.2, 2.3, 3.1) on Feb 26
7
Mar 3, 5, 7
3.3, 4.1, 4.2
Inverse of a matrix. Subspaces. Basis and dimension.
Application 4: encoding messages. Application 5: change of population distribution.
4.1: #1-15(odd),23,25,27,35,45-51(odd),57,65
4.2: #1,3,9,15,17,19,21
for grade: 4.1: #6,30,58, 4.2: #2,8,14,24
Q4, HW5 (3.2, 3.3) on Mar 7
8
Mar 10, 12, 14
4.2, 4.3
Null, row, and column spaces of a matrix. Rank-nullity theorem.
4.2: #25-31(odd),41,47-53(odd)
4.3: #1,3,9,11,15-33(odd),43,45,47,51-57(odd)
for grade: 4.2: #34,50, 4.3: #22,24,34,36
Q5, HW6 (4.1, 4.2) on Mar 14
9
Mar 24, 26, 28
5.1, 5.2, 5.3
Determinants and their applications.
Application 6: calculation of area.
5.1: #11,13,17,19,21,35,37,39,49,51,69-75(odd)
5.2: #3,7,11,13,25,35,39,47-57(odd),61;  5.3: #1,3,13,15,23,25
HW7 due Mar 28
10
Mar 31, Apr 2, 4
6.1, 3.5
Eigenvalues and eigenvectors. Application to the Markov process.
Application 7: population model.
6.1: #1,5,7,9,13,21,27,29,33,37-53(odd)
for grade: 5.2: #26(d),62; 5.3: #6; 6.1:#30,52; 6.3:#8
Exam2 (3.2, 3.3, 4.1, 4.2, 4.3, 5.1) on Mar 31
11
Apr 7, 9, 11
6.3, 6.4, 6.5
Change of basis. Diagonalization. Complex eigenvalues.
6.3: #1,5-17(odd),21,25,27,29
6.4: #5-15(odd),19,21,23,33,35,41;  6.5: #3,5,7
for grade: 6.4: #18,22,34; 6.5: #6;  extra credit: Application 8
Q6, HW8 (5.2, 5.3, 6.1, 6.3) on Apr 11
12
Apr 14, 16, 18
8.1, 8.2
Orthogonality, orthogonal complements, #8.1.69. Projections, Gram-Schmidt process.
8.1: #5(d),15,17,25-51(odd),65-71(odd)
8.2: #1-13(odd),23,25,27,29,37,39,41,51
for grade: 8.1: #32,34,42,44; 8.2: #30,54
HW9 due Apr 18
Withdrawal deadline: Apr 18
13
Apr 21, 23, 25
8.5, 7.1, 7.2, 7.3
Application 9: least squares solutions.
General vector spaces. Subspace, span, linear independence, basis.
8.5: #1,3,9,11,13, set the normal equation, but do not solve 35,37;   7.1: #13,15,19,23,25,27,41,43
7.2: #1-9(odd),17,19,21,25; 7.3: #1-9(odd),21-27(odd)
for grade: 8.5: #4,14; 7.1: #24; 7.2: #6,18; 7.3: #22
Q7 (6.4, 6.5, 8.1, 8.2), HW10 on Apr 25
14
Apr 28, 30, May 2
10.1
Exercises on diagonalization, orthogonality, and vector spaces. Inner product spaces.
10.1: #5,7,19,21,27,29,59,61,63,69,71
Exam3 (5.2, 6.1, 6.3, 6.4, 6.5, 8.1, 8.2, 8.5) on Apr 30,
HW11 on May 2
15
May 5, 7, 9
10.2, 10.3
Applications of inner products. Review.
Application 10: polynomial and Fourier approximations.
10.2: #2,8,10,15,16,21,23,37,39,41;   10.3: #11,15,17,25,35
16
Review exams, quizzes, homework.
Final Exam (topics of Exams 1,2,3; chapters 7,10) on May 14 (Wednesday), 10 am - 12 pm