Math 433, Summer 2013
Tentative Day by Day Schedule
for
the first part of the course
Part 1. Number theory and more.
06/03
. Greatest common divisor. Euclidean algorithm (section 1.1);
06/04
Greatest common divisor of several numbers, coprime numbers. Mathematical induction (section 1.1 continued, section 1.2);
06/05
Primes and the Unique Factorization Theorem (section 1.3)
;
06/06
Congruence classes and Modular Arithmetics (section 1.4)
;
06/07
Solving linear congruence (section 1.5)
;
06/10
Chinese Remainder Theorem, Fermat's little Theorem; Euler's theorem (section 1.6)
06/11
Euler’s totient function. Public key systems (section 1.6 continued);
06/12
Functions; Relations (section 2.1, 2.2, 2.3);
06/13
Finite State Machines (section 2.4);
06/14
Review before the first exam (chapters 1 and 2). Permutations (section 4.1)
06/17
The fir
st exam.
Part 2 Abstract Algebra
.
06/18
Order and sign of a permutation (section 4.2)
06/19
Sign of a permutation (continued). Abstract groups (section 4.2 continued and section 4.3)
06/20
Examples of groups (section 4.3 continued)
06/21
Further examples of groups. Semigroups.(section 4.3 continued, section 4.4)
06/24
Rings. Fields. Vector spaces over a field (section 4.4 continued)
06/25
Algebraic structures (section 4.4 continued).
06/26
Order of an element in a group. Subgroups (section 5.1)
06/27
Cyclic groups. Cosets. Lagrange's theorem (section 5.1 continued, section 5.2)
07/28
Subgroups (continued). Error-detecting and error-correcting codes (swection 5.2 continued, section 5.4)
07/01
Binary codes. Linear codes (section 5.4 continued)
07/02
Linear codes (section 5.4 continued). Classification of groups (section 5.3)
07/03
Review before the second exam (chapters 4 and 5)
07/05
The second exam. End of the course.