Instructor: David Nadler
Office Hours: Tuesdays 12:30-2pm, 740 Evans Hall, or by appointment.
GSIs
Lectures: Tuesdays and Thursdays 8:00-9:30am, 2050 Valley LSB.
Discussion sections: Wednesdays, see Times and Places
Course Control Number: 54180
Prerequisites: Math 54 or equivalent preparation in linear algebra.
Required text: Axler, Linear Algebra Done Right, second edition, Springer, 2nd edition (1997).
Grading policy: Based on homework (20%), in-class midterm (30%), and final exam (50%).
In-class midterm during lecture meeting: Thursday, October 24, 2013, Material: TBA
Final Exam: Wednesday, December 18, 2013, 3-6pm (Exam Group 11), in RSF Fieldhouse.
Academic honesty: You are expected to rely on your own knowledge and ability, and not use unauthorized materials or represent the work of others as your own. Protect your integrity and follow the honor code: "As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others."
There will be no make-up exams. No late homework will be accepted.
Grades of Incomplete will be granted only for dire medical or personal emergencies that cause you to miss the final, and only if your work up to that point has been satisfactory.
Homework is due Wednesdays. Please follow your individual GSI's instructions as to where to turn it in.
You are encouraged to discuss ideas with other students. However, you must write and hand in your solutions independently.
Each week, two selected problems from the homework assignment will be graded. Solutions to all problems will be posted.
When calculating grades, we will drop your two lowest homework scores and use only your remaining scores.
Chapter 1: problems 1, 3, 4, 6, 7, 8, 9, 13, 14, 15.
Additional problem: Find all subspaces of R^2. Be sure to justify your answer.
Chapter 2: problems 3, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16.
Additional problem: Suppose that W_1 and W_2 are subspaces of V and have basis sets B_1 and B_2 respectively. Suppose also that V is the direct sum of W_1 and W_2. Prove that the union of B_1 and B_2 is a basis for V.
Chapter 3: problems 1, 2, 3, 4, 5, 7, 8, 9, 10, 11.
Additional problem: Suppose that V is the direct sum of subspaces U_1 and U_2. Show that for W any vector space, L(U_1, W) and L(U_2, W) are naturally isomorphic to subspaces of L(V, W) and it is a direct sum of them.
Chapter 3: problems 12, 13, 14, 15, 16, 20, 22, 23, 24, 25, 26.
Additional problem: When does a 2x2 matrix with real entries give an isomorphism from R^2 to itself? Be sure to justify your answer.
Chapter 4: problems 1, 2, 3, 4, 5.
Additional problem: 1) Let V be a vector space over the complex numbers. Show that V is naturally a vector space over the real numbers by forgetting the possibility of scaling by imaginary numbers. 2) Suppose v_1, ..., v_n is a basis for V as a vector space over the complex numbers. Show that v_1, iv_1, ..., v_n, iv_n is a basis for V over the real numbers. 3) Calculate the matrix of the linear transformation T:V--->V given by scaling by 1+i with respect to the basis v_1, iv_1, ..., v_n, iv_n.
Chapter 5: problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Chapter 5: problems 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24.
Chapter 6: problems 1, 2, 3, 4, 5, 6, 7.
Chapter 6: problems 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
Chapter 6: problems 21, 22, 26, 27, 28, 29, 30, 31, 32.
Chapter 7: problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Chapter 8: problems 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13.
Chapter 8: problems 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 27, 28.
Some previous Math 110 course home pages:
George Bergman's notes: