Basic Mathematics - Algebra (SCI 113)

Lectures and exercise sessions :   Lectures:             Monday 15:45-17:30    lecturer: Dr. Ittay Weiss
Exercise session: Thursday 11:00-12:45  Stef Helsen, email: S.Helsen@students.uu.nl
                                                                 Julian Lyczak, email: J.T.Lyczak@students.uu.nl

Course Description

The elements of modern algebra (complex numbers, matrix algebra, determinants, vectors, linear transformations, and eigenvalues and eigenvectors) are presented with a strong algebraic flavour and applications and connection to other realms are mentioned in order to place the theory in a relevant modern context. With the concrete theory in place the course ends with a section abstracting the ideas presenting to get a glimpse at the notion of abstrat vector spaces - the heart of modern linear algebra.

Literature 

"Mathematical Techniques; An introduction for the engineering, physical, and mathematical sciences", D.W. Jordan and P. Smith

Testing and Evalution

The course is roughly divided into four parts. Each part is concluded with a hand-in assignment and a short test. The deadlines for the assignments and the test dates are indicated below. The assignments are to be handed in at the beginning of the exercise session to the TA. The graded assignments will be returned one week after the deadline. Each of the four tests lasts one hour (60 minutes). The graded tests will be returned one week after the test took place. The final grade for the course is the average of the four test grades and the four assignment grades. Participation in the tests and the handing in of the assignments is mandatory. Relief from any is only possible with a very good reason and in agreement with the lecturer beforehand.

Please note that not all handin assignments are of equal difficulty (though they do weigh equally for the grade). The first one is considerably less time consuming then the second. You should plan your time accordingly.

The handin assignments are designed to help you prepare for the periodical tests.

The handin assignments are to be handed in at the begining of the tutorial session as indicated below. You must submit your work in hard copy form (either printed or hand-written) in person to the tutors. Any other form of submission must be discussed with and approved by the tutors.

A note on writing mathematics: When giving an answer never give just a final result. Always explain how you got to that result. If you use a certain theorem or technique that was taught in class or appears in the book (which is perfectly fine) do clearly reference the source. So, one can start an answer to a specific problem by saying: employing the technique of complementary residual inverses to the complexified, saturated, and stratified case as shown in chapter 98 section 105.46 we calculate as follows....
Keep in mind that an answer should be a complete story with a beginning, middle, and ending. Avoid submitting a final answer that looks like some symbols jotted on a piece of paper.

Course Plan (some changes may occur)

WeekDate Session-no.Material to cover/Exercises to solveNotices
531-01-2011 Lecture 16.1 - 6.5: Complex Numbers Hand-in 1
03-02-2011Tutorial 1 Chapter 6: 2, 3, 5, 6, 7, 8, 9, 10, 19, 20, 25, 28
607-02-2011 Lecture 27.1 - 7.4: Matrix Algebra
10-02-2011Tutorial 2Chapter 7: 8, 13, 14, 17, 21
714-02-2011 Lecture 38.1 - 8.3: Determinants
17-02-2011Tutorial 3Chapter 8: 1, 2, 4, 8, 9, 12, 15
821-02-2011 Lecture 4First hour: Test 1 (on Lectures 1-3)
9.1 - 9.4: Vectors
Hand-in 2
24-02-2011Tutorial 4Chapter 9: 1, 2, 4, 5, 9, 12, 18 Deadline hand-in 1
928-02-2011 Lecture 59.5 - 9.6: Vectors (continued)
03-03-2011Tutorial 5Chapter 9: 21, 22, 23, 26, 36
1007-03-2011Lecture 610.1 - 10.6: The scalar product
10-03-2011Tutorial 6Chapter 10: 1, 3, 5, 11, 16, 27
1114-03-2011Lecture 710.7 - 10.9: The scalar product (continued)Hand-in 3
17-03-2011Tutorial 7Chapter 10: 28, 29, 34, 37, 38
1221-03-2011
Spring
Break

24-03-2011

1328-03-2011 Lecture 8First hour: Test 2 (on Lectures 4-7)
11.1 - 11.5: Vector product
31-03-2011Tutorial 8Chapter 11: 1- 7Deadline hand-in 2
1404-04-2011Lecture 912.1 - 12.5: Linear algebraic equations
07-04-2011Tutorial 9Chapter 12: 3, 4, 5, 7, 8, 9, 10
1511-04-2011Lecture 1013.1 - 13.2: Eigenvalues and eigenvectors
14-04-2011Tutorial 10Chapter 13: 1 - 7
1618-04-2011Lecture 11First hour: Test 3 (on Lectures 8-10)
13.3-13.5: Eigenvalues and eigenvectors - continued		Hand-in 4
21-04-2011Tutorial 11Chapter 13: 9 - 14Deadline hand-in 3
1725-04-2011Lecture 12No lecture (Easter) 

28-04-2011Tutorial 12Extra problems on eigenvalues
1802-05-2011Lecture 13Abstract vector spaces
Extra lecture notes
05-05-2011Tutorial 13No tutorial (Liberation Day) 
1909-05-2011Lecture14Continuation on abstract vector spaces
12-05-2011Tutorial 14All exercises from the lecture notes on abstract vector spaces
2016-05-2011Lecture 15Tying up loose ends + a perspective on modern mathematics

19-05-2011 Tutorial 15Test 4 (Note last test takes place during last tutorial session)Deadline hand-in 4