MATH 401: Introduction to Abstract Algebra
(Spring 2014)

List of the homework problems and the due dates

Multiple-page homework should be stapled. Otherwise it will not be graded.

Assignments are due at the beginning of the class on the indicated due date.

Abstract Algebra: A geometric approach by Theodore Shifrin, Prentice hall 1996.

• Homework assignment 1 (Due on January 22, in class)
  1.1, Integers, Mathematical induction and the Binomial theorem: pp. 8-11: 4d, 4j, 8a, 18
  1.2, Euclidean algorithm, Prime numbers and Factorization: pp. 17-20: 4b, 7, 12, 17

• Homework assignment 2 (Due on January 29, in class)
  1.3, Modular arithmetic and Solving congruences: pp. 30-36: 19, 20a, 22, 36
  1.4, Rings, Integral domains and Fields: pp. 41-44: 3, 9, 12, 13

• Homework assignment 3 (Due on February 7, in class)
  2.3, The Complex Numbers: pp. 64-67: 6a, 13a, 18, 19
  3.1, The Euclidean Algorithm: pp. 91-95: 6, 8, 10f, 14

• Homework assignment 4 (Due on February 26, in class)
  3.2, Roots of polynomials: pp. 102-105: 1, 3d, 5c, 6a
  3.3, Polynomials with integer coefficients: pp. 111-112: 2a, 3a, 7, 8
  4.1, Ring homomorphisms and ideals: pp. 122-125: 3, 6, 8, 9, 11, 16a, 18a

• Homework assignment 5 (Due on March 5, in class)
  4.2, Isomorphisms and fundamental homomorphism theorem : pp. 134-139: 5, 8, 9b, 13c, 13d, 14, 16a

• Homework assignment 6 (Due on March 21, in class)
  5.1, Vector spaces and dimension: pp. 153-159: 11b, 11g, 12, 17, 19
  5.3, An introduction to finite fields: pp. 168-169: 2, 3, 4, 5

• Homework assignment 7 (Due on April 4, in class)
  6.1, The basic definitions: pp. 178-181: 2a, 4, 10, 12, 17a, 23a
  6.2, Group homomorphisms and isomorphisms: pp. 185-187: 8, 9, 12, 13b, 13c

• Homework assigment 8 (Due on April 11, in class)
  6.3, Cosets, Normal subgroups and Quotient groups: pp. 196-200: 3, 6, 8, 13, 15, 19, 26a, 26b

• Homework assignment 9 (Due on April 21)
  7.1, Group actions on a set: pp. 219-221: 6, 14, 17, 18, 19
  7.5, Direct product, p-groups and Sylow theorem: pp. 259-262: 4c, 18, 27

• Homework assigment 10 (Due on April 25, in class: NOTE: we do have a make-up class on April 25)
  7.6, Some remarks on Galois theorey: pp. 277-282: 1b, 3, 9a, 12d, 12e, 22a

Last Modified January 31 (Friday), 2014.