Math 121 Spring 2005

Syllabus

This is a tentative schedule of lecture topics, exams and assignments. You are expected to read and study the text as we go along. Whether you study the text before or after the lecture is up to you; the best approach might be to do both. Assignments are due at the beginning of class on the indicated due date.

The assignments and handouts are PDF files which may be viewed or printed with a recent version of the free Adobe Acrobat Reader.

I stress that the exam times and assignment due dates indicated here are subject to change.

Date Topics Text Assignments
Thursday 13 January Introduction, conventions for notation, sets, truth tables 1.1, A.1 Assignment 1
(due 20 January)
Tuesday 18 January Induction, binomial theorem, infinity of primes, division algorithm 1.1, 1.2
Thursday 20 January g.c.d., Euclidean algorithm, fundamental theorem of arithmetic, congruence 1.2, 1.3 Assignment 2
(due 27 January)
Tuesday 25 January Modular arithmetic, divisibililty tests, applications: Diophantine equations, little Fermat 1.3, A.3 Quiz 1
Thursday 27 January The RSA cryptosystem 1.3 Assignment 3
(due 8 February)
Tuesday 1 February Solving congruence equations and systems of congruence equations; Z mod m 1.3, 1.4
Thursday 3 Febrary Rings, zero-divisors and integral domains, units and fields, examples 1.4
Tuesday 8 February Polynomial rings, division algorithm for polynomials over a field
Thursday 10 February Irreducibility of polynomials, g.c.d. 3.1 Assignment 4
(due 17 February)
Tuesday 15 February Euclidean algorithm for polynomials over a field, unique factorization of polynomials over a field 3.1
Thursday 17 Febrary Roots and field extensions 2.3, 3.2 Assignment 5
(due 24 February)
Tuesday 22 February Splitting Fields; Irreducibility of rational polynomials 3.2, 3.3 Quiz 2
Thursday 24 Febrary Rational root test, Gauss's lemma, reduction mod p 3.3 Assignment 6
(due 3 March)
Tuesday 1 March More reduction mod p, Eisenstein criterion
Thursday 3 March Ring homomorphisms 3.3 Assignment 7
(due 10 March)
Tuesday 8 March Fields as congruence clases of polynomials 4.1
Thursday 10 March Hour Exam Assignment 8
(due 24 March)
Spring Break
Tuesday 22 March Ring isomorphisms, ideals, fundamental homomorphism theorem 4.2 Midterm solutions
Thursday 24 March Transcendental vs. algebraic numbers 4.2 Assignment 9
(due 31 March)
Tuesday 29 March Gaussian integers 4.3
Thursday 31 March Unique factorization of Gaussian integers, application to primes of the form 4k+1 4.3 Assignment 10
(due 7 April)
Tuesday 5 April Vector spaces and dimension 5.1
Thursday 7 April Constructions with straightedge and compass 5.2 Assignment 11
(due 14 April)
Tuesday 12 April Impossibility of angle trisection with straightedge and compass 5.2
Thursday 14 April Symmetries of triangles and squares, groups, examples 6.1, 6.2 Assignment 12
(due 21 April)Quiz 3
Tuesday 19 April Subgroups, homomorphisms, isomorphisms 6.2
Thursday 21 April The strucure of the symmetric group 6.4
Tuesday 26 April The symmetric group and the 15-puzzle 6.4

Final Exam: Monday 2 May, 2-5PM, 120 Physics



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