MATH2301: Linear and Abstract Algebra and Number Theory

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Lectures

 

Chapter Topics Notes/Typos
Chapter 1 Number theory  
Chapter 2 Z/nZ Section 2.5 omitted
Chapter 3 Sets and Functions Ex 3.4.4, the log and exp example:  f o f^{-1} should be the identity on R^+ not on R\{0}.
Chapter 4 Semigroups  
Chapter 5 Groups Theorem 5.13.11 omitted, Section 5.14 omitted
Chapter 6 Rings  
     

 Linear Algebra printed notes

Slides:

1. Introduction to vector spaces (30/4/2010)

2. Subspaces (5/5/2010)

3. Span and linear dependence (7/5/2010)

4. Basis and dimension (10/5/2010)

5. Inner product spaces and orthonormal bases (12/5/2010)

6. Linear transformations (14/5/2010)

7. Matrix representation of a linear transformation (17/5/2010)

8. Isomorphisms (19/5/2010)

9. Change of basis/coordinates (21/5/2010)

10. Eigenvectors and eigenvalues (24/5/2010)

11. Diagonalisation (26/5/2010)

12. Cayley-Hamilton theorem (28/5/2010)

13. Jordan canonical form (31/5/2010)

14. Rational canonical form (2/6/2010) (Worked example from slide 16 -- here)

Exam Revision (4/6/2010)