Math 201 Linear Algebra - Fall 21 - Hans Lindblad

Announcements:

Description of the course

Description:Linear algebra is a collection of concepts and methods related to solving systems of linear equations: Gaussian elimination, matrix algebra, determinants. Linear subspaces, bases. Eigenvalues, eigenvectors, least-square, orthogonalty, diagonalization. Linear algebra has many applications to science/engineering; to electrical networks, economical models, chemical reactions, signal processing, statistics or numerical solution of differential equations.

Structure of course

Read the section of the text book (see schedule below).
Read the Lecture Notes (posted below before the lecture).
View the recorded Lecture segments at Blackboard.
Participate in the online zoom part of the lectures.
Participate in the in class TA sections.
Participate in your scheduled PILOT meetings.
Hand in your homework online.
Do four short quizzes in your section during weeks 2,4,8,12.
Do three online open-book midterms in weeks 6,10,15 (scheduled below).
Do a no book in person Final Friday, December 17, 9am-12pm in Shaffer 301, 303, 304.

Meetings

Lectures: MWF 10-11 online. Recorded lectures at blackboard 10-10.35 and live zoom meetings 10.35-10.50.
Instructor Hans Lindblad, lindblad@math.jhu.edu. Office hour F 11-12 online
Sections: Tu 1.30-2.20 Krieger 180: Head TA David Jaz Myers, dmyers40@jhu.edu, Office hour online F 2-3
Tu 3-3.50 Krieger 180, 4.30-5.20 Maryland 217: TA Yujie Luo, yluo32@jhu.edu, Office hour online M 4-5
Th 1.30-2.20, 3.00-3.50 Krieger 180: TA Akira Tominaga, atomina1@jhu.edu, Office hour online M 1-2
Th 4.30-5.20 Krieger 300: TA Cherlin Zhu, czhu27@jhu.edu, Office hour online M 2-3
PILOT meetingsPeer-Led Team Learning, Please Schedule
Learning DenSmall Group Tutoring
Math HelpRoom Online

Links for online meetings at blackboard. Attendance in live meetings required (Lectures, Sections, PILOT)

Texts and Online resources

Required Text: Bretscher Linear Algebra with Applications 5th ed

It is sometimes helps to get an alternative perspective. In the past I have taught from a different book that I think is easier to read Lay,Lay,McDonald Linear Algebra and Its Applications. The free online textbook Nicholson Linear Algebra with Applications seems to be good as well. I also like the online lectures at MIT by Strang. There is of course also Kahn Academy. There is also an animated Linear Algebra course 3Blue1Brown. There is a new online textbook Margalit,Rabinoff Interactive Linear Algebra. I can also be helpful and fun to learn to use Matlab to calculate with big matrices, see Instruction and Labs at UCSD. There is a new approach to teaching linear algebra Inquiry-Oriented Linear Algebra.

Schedule and Lecture Notes

The lecture notes below give my viewpoint of the material in the corresponding sections of this book. Although the lecture notes are self contained and cover most of the material you need to know the book contains more examples that may help build up your understanding. In particular the book often starts with a (real world) example whereas my notes often starts with the general case, due to limited time. Therefore it could be helpful to have a look at the corresponding sections in the book before the lectures.

Syllabus with list of sections of book covered:

Scedule (preliminary) with lecture notes posted the the day before:
wk  date  Monday  Wednesday  Friday
  1  8/30  1.1 Linear Systems  1.2 Gauss-Jordan Elimination  1.3 Vector and matrix equations
  2  9/6  Holiday  2.1 Linear Transformations    2.2 Geometric Transformations  
  3  9/13  2.3 Matrix Multiplication  2.4 Matrix Inversion  3.1 Image and Kernel
  4  9/20  3.2 Linear Independence, Basis  3.3 Basis, Rank theorem  3.4 Coordinates
  5  9/27  4.1 Vector Spaces  4.2 Isomorphisms  Review mid1f07 sol
  6 10/4  Review mid1s06 sol    Midterm I  4.3 Coordinate matrix
  7 10/11  5.1 Orthogonal Projection  5.2 Gram-Schmidt, QR Factor  5.3 Orthogonal Transformations
  8 10/18  5.4 Least Square Problems  5.5 Fourier Series  6.1 Determinants-definition
  9 10/25  6.2 Determinants-properties  6.3 Determinants-geometry  Review mid2f01 sol mid2s11 sol
10 11/1  Review mid2s14 sol mid2f14 sol  Midterm II  7.1 Diagonalization
11 11/8  7.2-3 Eigenvalues-Eigenvectors  7.3 Diagonalization  7.4 Dynamical Systems
12 11/15  7.5 Complex Eigenvalues  8.1 Symmetric Matrices  8.2 Quadratic Forms
13 11/22  Holiday  Holiday  Holiday
14 11/29  8.3 Singular Value Decomposition  Review fins06Q sol fins09Q sol  Review finf06Q sol fins05Q sol
15 12/6  Midterm III  Review fins06 sol fins09 sol  Reading Period
Note that the last review is during reading period

Assignments

Homework:
wk date  Homework (tentative) due Mondays 8 pm on Blackboard or GradeScope.  
  1  9/6  1.1: 12,14,16,20,28,46, 1.2: 4,10,18,26,38,44, 1.3: 4,14,22,28,36,58   
  2  9/13  2.1: 5, 8, 14a, 22, 36, 48, 50, 2.2: 2, 4, 10, 14, 18, 20, 24, 26de, 36,    
  3  9/20  2.3: 8, 17, 29, 50, 52, 82,  2.4: 8, 14, 20, 52, 60, 62, 84,  3.1: 10, 14, 24, 36, 44,    
  4  9/27  3.2: 2, 6, 14, 20, 24, 38,  3.3: 18, 20, 24, 30, 32, 68,  3.4: 14, 20, 28, 32, 38, 42,    
  5  10/4  4.1: 4, 10, 14, 26,  4.2: 10, 14, 28, 74,
 4.TF: 22, 34, 36, 38, 42, 46, 2.TF: 4, 28, 38, 44, 48, 60, 3.TF: 2, 6, 18, 24, 26, 52, 		 
  6 10/11  4.3: 1, 33, 55, 67, 69, 71,  
  7 10/18  5.1: 10, 16, 18, 20, 28, 30, 5.2: 2, 14, 16, 20, 28, 34, 5.3: 2, 28, 30, 40, 68, 70,  
  8 10/25  5.4: 4, 10, 14, 16, 20, 30, 5.5: 10, 12, 16, 26, 5.TF: 10, 12, 16, 26,  6.1: 8, 16, 30, 34, 44, 46,  
  9 11/1  6.2: 4, 6, 16, 18, 28, 40, 56, 68, 6.3: 2, 10, 18, 20, 24, 30, 6.TF 6, 12, 14, 18, 28, 46,  
10 11/8  7.1: 7, 15, 23, 37, 55, 71  
11 11/15  7.2: 4, 12, 14, 24, 26, 38, 7.3: 4, 8, 10, 14, 24, 38, 7.4: 2, 8, 10, 20, 28, 34  
12 11/22  Holiday  
13 11/29  7.5: 2, 12, 16, 30, 32, 44, 8.1: 6, 10, 12, 20, 24, 38, 8.2: 2, 6, 8, 14, 16, 18,      
14 12/6  8.3: 7, 11, 13, 21, 27, 35,    

Exams and Grading

Exams: Three online midterms and a final, four quizzes in sections.
Grade: Midterms each 12.5%, final 25%, quizzes 15% total, homework 15%, attendance 7.5%.
Attendance is based on a combination of attendance in PILOT, Sections and the live zoom part of the Lectures.

Practice Exams

Practice exams and solutions can be found at these previous iterations of the course Spring 2017 Spring 2021 and below:
mid1f01   mid1f01s   mid1f05   mid1f05s   mid1s06   mid1s06s   mid1s07   mid1s07s   mid1f07   mid1f07s   mid1s09   mid1s09s   mid1f09   mid1s10   mid1s10s  mid1f10   mid1f10s  mid1s11   mid1s11s  mid1s13   mid1s13s  mid1f13   mid1f13s   mid1s14   mid1s14s  mid1f15   mid1f15s  mid1s16   mid1s16s  mid1f16   mid1f16s  mid1s17   mid1s17s 
The old midterm 2 exams do not cover exactly the same parts of the course that we covered. Mostly it is that some of the exams cover eigenvalues which we have not done yet and some do not cover determinants that we have done. I made some midterm 2 review, for each exam, what is missing and what are things we have not covered.
mid2f01   mid2f01s   mid2f05   mid2f05s   mid2s06   mid2s06s   mid2f06   mid2s07   mid2s07s   mid2s09   mid2s09s   mid2s10   mid2s10s  mid2s11   mid2s11s  mid2s13   mid2s13s  mid2f13   mid2f13s   mid2s14   mid2s14s  mid2f14   mid2f14s  mid2f15   mid2f15s  mid2s16   mid2s16s   mid2f16   mid2f16s  mid2s17   mid2s17s 
Since there are no old midterm 3 I made some midterm 3 review, for each exam, which questions relate to the material covered in midterm 3, i.e. chapter 7, about eigenvalues, eigenvectors and diagonalization, and chapter 8 about symmetric matrices, quadratic forms and the singular value decomposition. (All of the sections 7.1-5, 8.1-3 can be on the midterm even if they are not respresented in the former exam problems below. It should however be covered in the homeworks for these sections, including the homework for section 8.3)
finf01   finf01s   fins02   fins02s   fins03   fins03s   finf03   finf03s   fins05   fins05s   finf05   finf05s   fins06   fins06s   finf06   finf06s   fins09   fins09s   finf13   finf13s   fins14   fins14s  finf15   fins16  
I like the Finals from Spring 2003, Fall 2003, Spring 2006, Fall 2006, and Spring 2009 the best.
Spring 2005, Fall 2015, Spring 2016 also have good problems but they do not cover as much, and there are no solutions for the last two.