Harvey Mudd College

Dept. of Mathematics

Math 63 – Linear Algebra II

Spring 2008 (First Half)

Prof. Susan Martonosi

 


ANNOUNCEMENTS:

* Review Linear Algebra I before the start of classes.  Here’s a review sheet to help you.

* Add yourself to the course email list.  Send an e-mail message to listkeeper@hmc.edu.  In the body of the e-mail message, write subscribe math-63-x-l  where x is your section number  (8am: Section 3; 9 am: Section 1; 10 am : Section 2).

* Please fill out the Student Information Form

 

HOMEWORK ASSIGNMENTS: Assigned daily; due weekly on Fridays at 5pm

 

HOMEWORK SOLUTIONS


PROF. MARTONOSI’S CONTACT INFO

Office: Olin 1277, extension 7-0481

E-mail: martonosi @ math . hmc . edu [please note the spelling…]

Office Hours: Monday 4:30-5:30; Wednesday 2:30-4 and Thursday 4-6 (also available by appointment)

 

Email is also a great way to get short questions answered quickly!

 

SECTION INFO

Section 3 – 8 am, MWF, TG 201

Section 1 – 9 am, MW, TG201; F, Galileo Edwards

Section 2 – 10 am, MWF, Beckman B126

 

AE HOURS

Sun, Mon, Thurs 8-10 pm in the LAC

 

COURSE GRADERS

Gena Urowsky, Ben Bergstedt, Edwin Lei, Bryce Lamp, Ross Merriam

 


 

COURSE OVERVIEW (click here for day-by-day)

This course is the follow-up to Math 12: Linear Algebra and Discrete Dynamical Systems I.  We will study similarity and diagonalization (with applications to estimating eigenvalues, solving systems of differential equations, Markov chains and linear recurrence relations); Orthogonality, complements, the Gram-Schmidt process, QR Factorization, the Spectral theorem and spectral decomposition; Vector spaces, including generalizing the notions of linear independence, basis, dimension and linear transformations seen in Math 12 and change of basis; Inner product spaces, norms, and applications to least squares.  Prerequisite: Math 12.  1.5 credit hours.

 

AIMS

This course is designed to develop your understanding of vectors, using a broader definition of “vector” than that explored in Math 12, and to prepare you for upper-division courses in mathematics, sciences and engineering.  Your understanding of linear algebra will be strengthened in two directions: 1. Thorough theoretical understanding of mathematical properties of vectors and matrices; 2. Practical understanding of applications of linear algebra to the sciences and engineering.  In addition to these content-related goals, an important aim of the course is to help you develop the critical thinking and reasoning skills necessary for you to become independent learners and thinkers.  Much of lecture material will be focused on proofs; indeed, manipulating sequences of known properties to demonstrate a previously unknown property is an excellent means to gain a profound understanding of the material and its uses.  The achievement of these ambitious goals depends on the continuous commitment of both you and your professor.

 

OBJECTIVES 

On completion of this course, you should be able to (among other things):

  1. Prove fundamental properties and theorems seen in class (including the Invertible Matrix Theorem), and use those theorems to prove simple extensions.
  2. Apply the theory to practical examples, such as identifying the dominant eigenvalue of a matrix, solving a system of linear differential equations, constructing an orthogonal basis, and others.
  3. Write clear solutions to mathematical problems, using appropriate definitions, counterexamples and proof techniques.

 



TEXT

Linear Algebra: A Modern Introduction, 2nd edition by David Poole.

Most of you probably have the 2nd edition from Math 12, but some of you may have the older 1st edition.  The two editions are nearly identical, but some differences exist, primarily in the exercises.  If you have the older edition, I urge you to double-check with a friend that you have done the correct homework problems before you turn in your homework.


HOMEWORK, EXAMS, GRADING

The purpose of homework is to give you practice and to help you absorb the material.  Exams let me evaluate how well you have done this.   Homework and exams together offer you opportunities to challenge yourself and to shine! 

 

Homework

The Homework page will list daily the reading and homework problems corresponding to that day’s lecture, but these problems will be collected together once weekly, on Fridays.  The best way to succeed in this course is to stay current by reviewing your class notes, reading the textbook and completing the homework problems after each lecture.  For other suggestions for success, please read these Study Tips.

 

            Grading rubric for homework assignments:

Each problem will be graded on a 5-point scale:

1 point:   Problem was attempted.
1 point:   Student approached the problem correctly, irrespective of technical mistakes that may have been made.
1 point:   Any assumptions made were stated (if this criterion is not applicable, then this point is a freebie for the student).
1 point:   The solution is correct.
1 point:   The writing and explanation are clear and easy to follow.

Under this rubric, it should be easy to get three points out of five (for attempting the problem, stating assumptions and writing clear explanations).  Moreover, a correct solution might earn only three points out of five if assumptions are not stated clearly or if the writing and explanation are unclear.  So I feel this scheme puts weight on the things I'd like most to encourage. 

 

-          Homework will be due on Fridays at 5pm.

-          No late homework will be accepted without a note from a Dean.

-          Homework must adhere to the Mathematics Department Homework Guidelines format described at http://math.hmc.edu/~orrison/teaching/homework/

-          Homework solutions will be posted here.

-          Honor Code: You are encouraged to discuss your homework assignments with your classmates, but each student must write up his or her own solutions individually, and must acknowledge any assistance given or received.  Harvey Mudd's honor code applies in all matters of conduct concerning this course.

 

Exams

There will be two exams:

-          Midterm (Take-Home)– handed out Friday 2/8 and due Sunday 2/10 at 11:59 pm

-          Final (In-Class)– Friday 3/7

-          Honor Code: All exams are strictly confidential; no cooperation is allowed. 

 

Final Grade:  Homework – 30%; Midterm – 30%; Final – 40%.  However, you must receive credit on at least half of the homework assignments in order to pass the course.

 

NOTE: If you need disability-related accommodations, please discuss this with Dean Noda as soon as possible.

 

STUDENT FEEDBACK

In addition to formal mid-course and end-of-course evaluations, I encourage you to let me know immediately after class if a concept was not clear or if there is something I can do to facilitate the learning process in class.  And if you are struggling with the course, the best way to let me know is to come to my office… frequently.  I am here to help you learn the material, but I cannot do so if you do not actively seek help.