Summer Session II 2006 MAT 312 (AMS 351)
What to study for the Final Exam
Applied Algebra
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Instructor |
Daniel An danan@math.sunysb.edu
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Time/Place |
Monday, Wednesday and Thursday 6:00PM to 8:15PM @ Physics P116 |
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Grader |
Lena Panok lena@math.sunysb.edu
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Textbook |
Textbook: Numbers,
Groups and Codes (2nd ed.), J. F. Humphreys, M. Y. Prest, Cambridge University Press To buy this book check AddAll |
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Grading |
Homework(15%) Project(10%) Midterm(30%) Final(45%) |
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Prerequisites |
1. MAT 203 or MAT 205 or AMS 261 (Multivariable Calculus) |
Homeworks (All homeworks will be graded out of 15. Easier problems will worth fewer points.)
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Due |
Homework (Problems are from the textbook) |
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1 |
Wednesday July 19th 2006 |
1.1 1-(iv),5,6 1.2 5,8,9 |
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2 |
Wednesday July 26th 2006 |
Take your time to read through Chapter 1.3 to 1.5 Also send a email containing your full name, to danan@math.sunysb.edu so that I can assign you the first project. The projects will only be assigned through email, so be sure to email! |
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3 |
Monday July 31st 2006 |
1.3 6 (hint) 1.5 4-(ii) 1.6 1-(iii),2-(iv),6,10 |
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4 |
Monday |
2.3 5,6,7,8 4.1 3,4 3.1 3 (You will probably want to do 2.3 and 4.1 before midterm 1!) |
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5 |
Wednesday Aug 16th 2006 |
3.3 1 4.2 1-(ii), 4, 5,7,13 (Just for fun : Google Noyes Chapman's fifteen puzzle for the historical account of this problem) 4.3 1-(v),1-(viii) |
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6 |
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To be announced (or may not be assigned.) |
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7 |
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To be announced (or may not be assigned.) |
Syllabus
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Date |
Material to be covered |
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July |
12 |
1.1 The division algorithm and greatest common divisors |
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13 |
1.2 Mathematical Induction |
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17 |
1.3 Primes and unique factorisation Theorem 1.4 Congruence classes |
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19 |
1.4 Congruence classes (cont'd) |
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20 |
1.5 Solving linear congruences |
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24 |
1.6 Euler's Theorem and public key codes (Project 1) |
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26 |
2.1 Elementary set theory 2.2 Functions |
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27 |
2.2 Functions (cont'd) 2.3 Relations |
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31 |
4.1 Permutations |
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Aug |
2 |
overview of 3.1 Propositional logic and 3.3 Some proof strategies |
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3 |
Midterm Exam |
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7 |
4.2 The order and sign of permutations |
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9 |
overview of 4.3, 4.4, 5.1, beginning of 5.3 |
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10 |
5.2 Cosets and Lagrange's Theorem |
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14 |
5.3 Groups of small order 5.4 Error-detecting and error-correcting codes |
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16 |
5.4 Error-detecting and error-correcting codes (cont'd) |
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17 |
Review |
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21 |
Final Exam |