Homepage for MAS212 - Linear Algebra - Spring 2011

Syllabus and course information.

Please come see me if you have any questions.

Office Hours: M-W-F: 15.00 - 16.00.

If these times are not convenient just make an appointment by email or phone!

Office: E6-1 4411

Email: andreash[at]kaist.edu

Phone: 350 7300

Lectures

NOTICES

• May 28 - 30: CLAIMS for Final exam and course grade.
• May 27 : FINAL EXAM. See notice below.
• May 10: Holiday. Recitation classes moved to Thursday 5/12. (Note room change.) Same time: 5 - 6pm room 412 (bldg E11), 7 - 8pm room 304 (bldg E11).
• No Class Friday May 6th.
• April 29: Quiz 7.
• Apr 22: QUIZ 6.
• April 11: Class cancelled
• NO QUIZ on Friday 4/8!
• April 1: MIDTERM. Rooms: 1412, 1501, 3433 (E6-1). Time: 10-12 am. (DETAILS BELOW)
• Mar 30: SPECIAL RECITATION CLASS. 7pm -9pm, Room 309 (E11). (Different room than usual!!)
• Mar 25: NO CLASS
• Mar 18: QUIZ 4.
• Mar 11: QUIZ 3.
• Mar 4: QUI 2.
• Mar 1: Holiday. Recitation classes moved to Thursday 3/3. Same time, room 304 (bldg E11).
• Feb 25: First quiz in class.
• Feb 22: Recitation classes will start on Tuesday Feb 22.
• Feb 16: Lecture cancelled on Feb 16. Reason: KAIST anniversary.

FINAL EXAM

Here are score files of the FINAL EXAM.

Solutions: 1 2 3 4 5 6

Claims for the final exam will take place Sunday 5/29: 6pm to Midnight, and Monday 5/30: 11 am to 6pm and 7pm to 9pm. You may come to my office: 4411 to review your exam.

The FINAL EXAM is scheduled for May 27, 10.00am - 12.30pm. The room you will take the FINAL EXAM depends on your student ID (see below). Arrive at 9.50.

Scope of the FINAL EXAM will be chapters 6 and 7. (Note that the material of these chapters builds on the theory developed in previous chapters!! )

The FINAL EXAM will take place in three different rooms. The room you will take your midterm depends on your STUDENT ID NUMBER. All rooms are in buidling E6-1

• Room 3433: Id numbers : 20040441 - 20090770.
• Room 1412: Id numbers : 20090818 - 20100395.
• Room 1501: Id numbers : 20100409 - 20110962.

Notice!

• You will arrive on time to the exam.
• You will bring only writing material to your desk: pencil, pen, eraser.
• You will not bring any of the following items to your de$ papers, books, bags, calculator.
• CELL PHONES will be turned off at all time during the exam.

The Finals will be graded on May 27 and 28. Claims will be from May 29 to 30.

MIDTERM EXAM

Here are score files and statistics of the midterm.

Midterm exam is scheduled for April 1, 10-12 am. The room you will take the midterm depends on your student ID (see below). Arrive at 9.50.

Scope of the midterm exam will be chapters 1, 2, 3.

The midterm will take place in three different rooms. The room you will take your midterm depends on your STUDENT ID NUMBER. All rooms are in buidling E6-1

• Room 3433: Id numbers : 20040441 - 20090770.
• Room 1412: Id numbers : 20090818 - 20100395.
• Room 1501: Id numbers : 20100409 - 20110962.

Notice!

• You will arrive on time to the exam.
• You will bring only writing material to your desk: pencil, pen, eraser.
• You will not bring any of the following items to your desk: papers, books, bags, calculator.
• CELL PHONES will be turned off at all time during the exam.

Specieal recitation class. There will be a special recitation class during midterm week: 7pm - 9pm in room 309 in the creative learning building (E11). (Note that it is a different room than usual!)

RECITATION CLASSES

There will be 3 recitation classes. All recitation classes will take place in the Creative Learning Building E11, Room 412.

Class 1 : Tuesday, 17.00 -- 18.00

Class 2 : Tuesday, 19.00 -- 20.00

Class 3 : Wednesday, 19.00 -- 20.00

Class 4 : Wednesday, 20.00 -- 21.00

In the recitation classes we will cover suggested problems and answer questions about the material covered in the lectures.

Every student must sign up for one of the classes!

QUIZZES

There will be weekly quizzes. They will start in the 3rd week of class.

• Quiz 1: Friday 2/25. Ch 1.1 - 1.6
• Quiz 2: Friday 3/4. Ch 2.1 - 2.4
• Quiz 3: Friday 3/11. Ch 3.1 - 3.2
• Quiz 4: Friday 3/18. Ch 3.3 - 3.6
• Quiz 5: Friday 4/15. Ch 5.1 - 5.3
• Quiz 6: Friday 4/22. Ch 6.2 - 6.3
• Quiz 7: Friday 4/29. Ch 6.4 - 6.6

Suggested problems

There will be weekly quizzes and suggested homework (problems given on the quiz will be the same or similar to the suggested homework). Below is a list of suggested problems to be covered in quizzes and recitations. It is recommended to try to solve every problem in the book.

• Chapter 1:
  • Sec 1.2 : Exs 1 , 4 , 5 , 6 , 7 , 8.
  • Sec 1.3 : Exs 2 , 3 , 5 , 6 , 7 , 8.
  • Sec 1.4 : Exs 2 , 4 , 8, 10.
  • Sec 1.5 : Exs 3 , 4 , 5 , 6 , 7 , 8.
  • Sec 1.6 : Exs 4 , 5 , 7 , 9 , 10 , 12.
  
  
• Chapter 2:
  Sec 2.1 : Exs 3 , 4 , 6 , 7
  • Sec 2.2 : Exs 2 , 3 , 5 , 7
  • Sec 2.3 : Exs 5 , 6 , 7 , 9 , 13
  • Sec 2.4 : Exs 3 , 4 , 5 , 6 , 7
  • Sec 2.6 : Exs 1 , 2 , 3 , 4 , 5 , 6 , 7
• Chapter 3:
  • Sec 3.1 : Exs 1 , 3 , 4 , 5 , 7 , 9 , 10 , 12 , 13
  • Sec 3.2 : Exs 1 , 3 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
  • Sec 3.3 : Exs 2 , 3 , 4 , 6 , 7
  • Sec 3.4 : Exs 2 , 3 , 4 , 8 , 9 , 11 , 12
  • Sec 3.5 : Exs 1 , 2 , 3 , 4 , 7 , 8 , 10 , 11
  • Sec 3.6 : Exs 1 , 2
  • Sec 3.7 : Exs 1 , 3 , 4 , 6 , 7
• Chapter 5:
  • Sec 5.2: Exs 1 , 3 , 4 , 5 , 6 , 7 , 11 , 12 , 13
  • Sec 5.3: Exs 1 , 2 , 4 , 5 , 6 , 8 , 9 , 10 , 11 , 13
  • Sec 5.4: Exs 3 , 4 , 5 , 7 , 9 , 10 , 11 , 14
• Chapter 6:
  • Sec 6.2: Exs 1 , 2 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 13
  • Sec 6.3: Exs 1 , 2 , 3 , 4 , 5 , 6 , 8 , 9
  • Sec 6.4: Exs 1 , 2 , 3 , 4 , 5 , 7 , 8 , 9 , 10 , 11 , 13
  • Sec 6.6: Exs 1 , 2 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11
  • Sec 6.7: Exs 1 , 3 , 4 , 6 , 8 , 9
  • Sec 6.8: Exs 1 , 2 , 3 , 4 , 5 , 7 , 8 , 9 , 11 , 13
• Chapter 7:
  • Sec 7.1: Exs 1 , 2 , 4 , 6 , 7
  • Sec 7.2: Exs 2 , 3 , 4 , 7 , 11 , 13 , 18
  • Sec 7.4: Exs 1 , 2 , 4 , 5

Weekly progress

• Week 1:
  • Appendix: Sets, functions, relations.
  • Sec 1.1 - 1.3: Fields, systems of linear equations, matrices.
  
  
• Week 2:
  • Sec 1.3 - 1.4: Row operation, row equivalence, row reduced matrices.
  • Sec 1.5 - 1.6: Elementary matrices, matrix multiplication.
  
  
• Week 3:
  • Sec 1.6 : Invertible matrices.
  • Sec 2.1 - 2.2 : Vector spaces, subspaces.
  • quiz
  
  
• Week 4:
  • Sec 2.2: Subspaces, linear span, linear combinations.
  • Sec 2.3: Linear independence, bases, dimension.
  • Sec 2.4: Coordinates with respect to basis, transition matrix
  • Sec 2.5: Vector spaces and row operations.
  • quiz
  
  
• Week 5:
  • Sec 3.1: Linear transformations, null space and rank.
  • Sec 3.2: Algebra of linear transformations, the space L(V,W).
  • Sec 3.2: Compositions, linear operators, invertible transformations.
  • Sec 3.3: Isomorphism of vector spaces.
  • Sec 3.4: Matrix representation of linear transformations, similar matrices.
  • quiz
  
  
• Week 6:
  • Sec 3.5: Linear functionals, the dual space, annihilators.
  • Sec 3.6: The double dual isomorphism.
  • Sec 3.7: The transpose.
  • quiz
  
  
• Week 7: Review of chapters 1, 2, 3.
  
• Week 8: MIDTERM
  
• Week 9:
  • Sec 5.1: Rings, groups, fields.
  • Sec 5.2: n-linear functions, determinant functions.
  • Sec 5.3: Uniqueness of the determinant function, permutations.
  • Sec 5.5: Modules.
  
  
• Week 10:
  • Sec 6.1: Elementary canonical forms.
  • Sec 6.2: Diagonalizable operators, characteristic polynomial.
  
  
• Week 11:
  • Sec 6.3: Annihilating polynomials, the minimal polynomial.
  • Sec 6.4: Invariant subspaces, triangulable operators, minimal polynomial, diagonalizable operators.
  
  
• Week 12:
  • Sec 6.6: Direct sum decomposition, projections.
  • Sec 6.7: Invariant direct sums.
  • Sec 6.8: The primary decomposition theorem.
  
  
• Week 13:
  • Sec 6.8: Examples using the primary decomposition theorem.
  • Sec 7.1: Cyclic subspaces.
  
  
• Week 14:
  • Sec 7.1: Cyclic subspaces, companion matrix.
  • Sec 7.2: Cyclic decomposisition theorem, the rational form.
  
  
• Week 15:
  • Sec 7.4: Computing invariant factors.
  • Sec 7.3: The Jordan form.
  
  
• Week 16: FINAL