Math 121  Spring 2005 
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, zerodivisors 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 15puzzle  6.4 