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Week 1 | |
| Mon (March 30) |
Sec 26 Ring homomorphisms and ideals.
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| Homework |
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| Wed (April 1) |
Sec 26: Quotients and fundamental homomorphism sequence.
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| Homework |
Ex 26 (p.243-245): 1($), 3, 5, 6, 7, 10, 12($), 13($), 17 ($), 18, 20, 21 ($), 25, 28($), 30($), 34, 36, 37.
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| Fri (April 3) |
Sec 27:
Maximal ideal.
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| Homework |
Ex 27 (p. 252-254): 15($), 18, 19, 34, 35($), 36($), 37($), 38($),
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Week 2 | |
| Mon (Apr 6) |
Sec 27: Prime ideals.
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| Homework |
Ex 27 (p. 242-254): 2($), 4($), 7($), 8, 16($), 17, 25($), 32($).
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| Wed (Apr 8) |
Sec 45: Irreducible elements, PID's and UFD's.
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| Homework |
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| Fri (Apr 10) |
Sec 45: PID's and UFD's.
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| Homework |
Ex 45 (p. 399-401): 10($), 21, 26($), 27, 33($), 34($).
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Week 3 | |
| Mon (Apr 13) |
Section 45More on UFD's.
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| Homework |
Ex 45: 12, 29, 31($).
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| Wed (Apr 15) |
Section 45 & 46:Euclidean domains. Euclidean algorithm.
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| Homework |
Ex 46: 6($), 7, 9($), 12, 13, 16, 17($), 20, 21($), 22($), 23, 24($).
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| Fri (Apr 17) |
Section 47Gaussian integers.
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| Homework |
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Week 4 | |
| Mon (Apr 20) |
Section 29 Extension fields.
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| Homework |
Ex 47: 1, 2($), 5($), 7($), 8, 9($), 10 ($), 13($), 15(a)&(b), 15(c)(i)&(ii), 16
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| Wed (Apr 22) |
Section 29 Extension fields.
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| Homework |
Ex 29: 2($), 4, 5($), 7, 8, 13($), 11-12-13-14-15-16, 17, 18($), 22, 24, 25($), 30($), 31($), 32($), 33, 35, 36.
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| Fri (Apr 24) |
Introduction to linear algebra.
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| Homework |
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Week 5 | |
| Mon (Apr 27) |
Chapter 1.A Vector spaces.
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| Homework |
Ex 1.A (p 13-15): 1, 2($), 3($), 4, 5, 7, 9.
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| Wed (Apr 29) |
Chapter 1.B Linear maps and algebra of endomorphisms.
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| Homework |
Ex 1.B (P 20): 2($), 3, 5($), 6($), 7($).
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| Fri (May 1) |
Midterm.
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| Homework |
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Week 6 | |
| Mon (May 4) |
Chapter 1C Linear independence and basis.
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| Homework |
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| Wed (May 6) |
Chapter 1C Linear independence and Basis.
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| Homework |
Ex 1C (p. 27-28): 2($), 3 ($), 4, 5, 6($), 7, 8, 9($), 10($), 11($).
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| Fri (May 8) |
Chapter 1D Direct sums.
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| Homework |
Ex 1D (p. 35-36) : 1, 4($), 6($), 7($).
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Week 7 | |
| Mon (May 11) |
Chapter 1D Quotients. Geometry of R^3.
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| Homework |
Ex D (p. 35-36): 3($), 5.
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| Wed (May 13) |
Chapter, 1E, 1F Eigenvalues and Eigenvectors (i), Hom space and dual.
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| Homework |
Ex E(p. 40-41): 2, 3($), 4($), 6, 7($), 8, 9($).
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| Fri (May 15) |
Ch 2A Matrices.
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| Homework |
Ex 1F (p. 45-46): 3($), 5, 6, 7($), 8, 9($), 10.
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Week 8 | |
| Mon (May 18) |
Ch 2A Adjoint of a transformation and rank of a matrix.
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| Homework |
Ex 2A (p 54-56): 2, 3($), 5, 6(i), 6(ii)($),
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| Wed (May 20) |
Ch 2B-2C The exterior algebra of R^n.
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| Homework |
Ex 2B (p 61): 1 ($) (Please read p. 56-60 before doing this problem. We have already done the
general case in class).
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| Fri (May 22) |
Ch 2C-2D Determinants. Inverses and Systems of Equations.
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| Homework |
Ex 2C (p. 65-66): 2($), 3.
Ex 2C (p 68-70): 3($), 4($), 5($), 6, 7($), 8, 9, 10($), 11(ii)($)
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Week 9 | |
| Mon (May 25) |
Memorial day.
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| Homework |
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| Wed (May 27) |
Ch 2E-3B Eigenvalues (part (ii)). Minimal polynomial.
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| Homework |
2D (P 75-76): 2, 3, 4(ii), 5, 6, 7, 8
3E (p 79-80): 3, 4
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| Fri (May 29) |
Ch 3A-3C The characteristic polynomial. Cayley Hamilton theorem.
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| Homework |
3A (p 85-86): 5(i), (ii), (iii), 7, 8.
3B (p 93): 2, 9, 10,
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Week 10 | |
| Mon (June 1) |
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| Homework |
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| Wed (June 3) |
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| Homework |
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| Fri (June 5) |
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| Homework |
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