n UC Berkeley Math 110: Linear Algebra n

Math 110: Linear Algebra (Spring 2011)

Department of Mathematics
University of California, Berkeley
Description: Vector spaces. Linear transformations and matrices. Linear systems of equations. Determinants. Eigenvalues and eigenvectors. Inner product spaces. Self-adjoint, normal, and unitary maps. Canonical forms. Course control number: 54251.
Lecturer: F. Alberto Grunbaum, grunbaum@math.berkeley.edu, 903 Evans, Phone (510) 642-5348
Office hours: Tue 10:00am - 11:30am and Th 10:00am - 11:30am in 903 Evans
Lectures: Tu-Th 8-9.30am, Room 145 Dwinelle
Textbook: S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra, 4th edition, Prentice Hall, 2002 (Amazon).
  • As you can see from the syllabus I intend to go rather fast at the beginning and reserve more time to cover material with which you are less familiar.
  • This class has elements in common with Math 54, but the emphasis on proving things and understanding things at a deeper level is very important. Here is a list of topics that should indicate some of the differences with Math 54. Some of the topics below we will cover in detail, some will be discussed briefly.
  • Gaussian elimination and LU factorization.
  • Matrix limits and Markov chains
  • Least square problems
  • Gram-Schmidt and QR factorization
  • Singular values and vectors
  • Solving difference and differential systems of linear differential equations. The use of spectral methods. Coupled harmonic oscillators.
  • Spectral methods used to solve nonlinear evolution equations such as coupled unharmonic oscillators.
  • On the first day I intend to give a "bird's eye" view of the entire course so that you will see where it stands vis-a-vis material that you have already seen in the past.
  • In this class, as in any upper division math class there is only one way to learn the material: you need to read the book very closely, making sure that you understand every step of the argument in the book. There is no way that I can go through every argument in lecture, but I expect you to read the book before and after class.
  • I strongly encourage people to form small (3-4 people at most) study groups and meet 2 or 3 times a week starting on week one. Each one of the members of the group should try to explain to the others what she/he feels they understand well. In many cases you will discover that you thought you understood...but in fact you did not. That step is a good and useful one. You should question each other, talk about the homework, reread the material in the book that is relevant and make sure that things become clear.
  • Homework will be assigned weekly and eventually we will reach steady state at about 15 problems per week. Your GSIs will select every week around 4 problems and grade these. Your homework grade will result from a combination of points for attempting all the problems and then doing well in the ones that are selected for grading.
  • Homework will be graded out of 15 points. 3 points will be given for completion, the other 12 points will be given for doing well in the ones that are selected for grading. No points will be given if the homework is not the in the required format: (1) Use blank, white paper and pen (or LaTeX). (2) Only one side of each sheet of paper may be used, and each page should only have work for one problem (unless the student has used LaTeX). (3) Solutions must be written in complete sentences. Standard mathematical symbols are perfectly acceptable, but these symbols stand for words which must fit into a complete sentence.
  • One of the best ways to learn the material is to take the homework very seriously. Nobody should be surprised if some of the problems that have been assigned during the semester show up in the midterm or even in the final.
    • Announcements:
    Homework:
    HW Date Problems Solutions
    01 Wed 01/26 1.2: 1, 16, 19
    1.3: 8ce, 9, 11, 23, 30
    1.4: 5aeg, 10, 12, 15
    1.5: 1, 3, 5, 7
    1.6: 8, 13, 22
    		 PDF
    02 Wed 02/2 2.1: 12, 16, 21
    2.2: 2, 10
    2.3: 8, 13
    2.4: 3, 16
    2.5: 4, 6ac, 11
    2.7: 3, 13, 18     		PDF
    03 Wed 02/9 2.1: 5 , 6 , 14
    2.2: 5ab
    2.5: 3ab
    3.1: 2, 3
    3.2: 4, 5, 20
    3.3: 2(all)
    3.4: 2(a,c,e), 5, 6
    		 PDF
    04 Wed 02/23 4.1: 4 c,d
    4.2: 3 , 12 , 22
    4.3: 1 , 4, 22, 24
    4.4: 3 f,g,h, 4 f,g,h
    		PDF
    05 Wed 03/2 5.1: 1(all), 2(d) ,4(h,i,j), 7 , 22, 23
    5.2: 1, 2, 7, 14, 18
    		PDF
    06 Wed 03/9 5.3: 1 (all), 2 (g,i) 7
    5.4: 1 (all) , 2 (all), 3 (all), 4 , 6, 17, 19, 22
    		PDF
    07 Wed 03/16 6.1: 1, 2, 3, 9, 11, 12 ,13, 16, 19, 21, 24, 26
    6.2: 2h, 2i ,3, 6, 9, 15, 22
    		 PDF
    08 Wed 03/30 6.3: 1, 3, 7, 10, 12, 21, 22a , 23
    6.4: 1, 2, 3, 4, 6, 7
    		 PDF
    09 Wed 04/06/2 6.5: 1, 2, 17, 21, 29
    6.6: 1, 3, 5, 6, 8
    		 PDF
    10 Wed 04/13 6.7: 1, 3(a,b,e), 6(a,b,e)
    		 PDF
    11 Wed 04/20 6.7:4, 8, 9, 11, 16
    		 PDF
    12 Wed 04/27 7.1: 1(all), 3(all)
    7.2: 1(all), 3(all), 17, 20, 22
    7.3: 1(all), 2(all), 3, 4, 8, 9
    		 PDF
    Syllabus:
    Lec Date Topic Other
    01 Tu 01/18 Overview of the class  
    02 Th 01/20 Chapter 1  
    03 Tu 01/25 Chapter 2  
    04 Th 01/27 Chapter 2  
    05 Tu 02/01 Chapter 2
    06 Th 02/03 Chapter 3  
    07 Tu 02/08 Chapter 3
    08 Th 02/10 REVIEW
    09 Tu 02/15 FIRST MIDTERM  
    10 Th 02/17 Chapter 4  
    11 Tu 02/22 Chapter 5
    12 Th 02/24 Chapter 5  
    13 Tu 03/01 Chapter 5  
    14 Th 03/03 Chapter 5
    15 Tu 03/08 Chapter 5  
    16 Th 03/10 Chapter 6  
    17 Tu 03/15 Chapter 6  
    18 Th 03/17 Chapter 6  
    19 Tu 03/22 SPRING BREAK  
    20 Th 03/24 SPRING BREAK  
    21 Tu 03/29 Chapter 6  
    22 Th 03/31 Chapter 6  
    23 Tu 04/05 Chapter 6
    24 Th 04/07 Chapter 6  
    25 Tu 04/12 SECOND MIDTERM  
    26 Th 04/14 Chapter 7
    27 Tu 04/19 Chapter 7  
    28 Th 04/21 Chapter 7  
    29 Tu 04/26 Chapter 7
    30 Th 04/28 Chapter 7  
    31 >Tu 05/03 RRR WEEK  
    32 Th 05/05 RRR WEEK  
      Th 05/12 Final Exam - 7-10pm Final Exam
    GSIs and Discussion Sections:
    Sec Time Room GSI E-mail Office Office hours
    01 Wed 9am-10am 4 Evans I. Ventura iventura@math.berkeley.edu
    02 Wed 10am - 11am 56 Hildebrand C. Mitchell cmitch5@math.berkeley.edu
    03 Wed 11am - 12pm 246 Dwinelle I. Ventura iventura@math.berkeley.edu
    04 Wed 8am - 9am 71 Evans I. Ventura iventura@math.berkeley.edu
    05 Wed 2pm - 3pm 116 Haviland E. Wayman ewayman@math.berkeley.edu
    06 Wed 12pm - 1pm 256 Dwinelle C. Mitchell cmitch5@math.berkeley.edu
    07 Wed 1pm - 2pm 6 Evans E. Wayman ewayman@math.berkeley.edu
    08 Wed 3pm - 4pm 2030 Valley LSB C. Mitchell cmitch5@math.berkeley.edu
    Grading and policies: Homework: There will be weekly homework. Collaboration on the homework is allowed (but not encouraged), and each student must write his/her own solutions and not copy them from anyone else. Only some of the problems from each homework will be graded. Late homework will not be accepted, but the two lowest scores will be dropped when computing the grade.

    Exams: There will be two in-class midterm exams, scheduled for TUESDAY Feb 15 and TUESDAY April 12 between 8.10 am - 9.30 am. The final exam will be given on THURSDAY May 12 between 7pm - 10pm. The exams are "closed book". In particular, you may not bring textbooks, notebooks, or calculators. If there is an emergency alarm during the midterms or the final exam, leave the exam at the desk and walk out. You may of may not be allowed back to complete the work.

    Grade corrections: The grades for the exams will be changed only if there is a clear error on the part of the grader, such as adding up marks incorrectly. Problems must be brought to the attention of the GSI immediately after the exams are returned.

    Grades: The final grade will be based on weekly homework assignments (30%), Midterm 1 (15%), Midterm 2 (20%), and the Final Exam (35%).
    If you miss the first midterm the grade for the second midterm will count 35%. If you miss the second then the grade for the final will count for 55%. If you miss both midterms or the final, then you will fail the class. There will be no makeup exams or quizzes.
    Incomplete grades: Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or genuine personal/family emergency. Falling behind in this course or problems with workload in other courses are not acceptable reasons.

    Special arrangements: If you are a student with a disability registered by the Disabled Student Services (DSS) on UCB campus and if you require special arrangements during exams, you must provide the DSS document and make arrangements via email or office hours at least 10 days prior to each exam, explaining your circumstances and what special arrangements need to be done. Also see your GSI as soon as possible if you need special arrangements during the sections or for submitting the homeworks.