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What's new!
o Dec. 6: Just posted an info sheet for final exam as well as solutions to MT2. |
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Weekly homework and other online material
Final exam info sheet Solutions to midterm 2 HW6: Due Wednesday November 28 Sec. 8.4: 1, 4 Sec. 9.1: 4, 8, 12 Sec. 9.2: 6, 9 Sec. 9.3: 14 Midterm 2 info sheet HW5: Due Wednesday November 7 Sec. 6.2: 2 Sec. 6.3: 6, 10 Sec. 7.1: 6, 41 Sec. 7.2: 2, Sec. 7.4: 10 Solutions to midterm 1 HW4: Due Wednesday October 24 Sec. 4.2: 2(e), 14(d) Sec. 4.3: 4(b), 22 Sec. 4.4: 2(c), 10 Sec. 6.1: 10, 28 Midterm 1 info sheet HW3: Due Wednesday October 3 Problem: Bertrand's postulate asserts that for any integer x greater than 1 there is a prime number p between x and 2x. Use this to show that any positive integer n greater than 7 is a sum of distinct primes. Sec. 3.4: 3(d), 19 Sec. 3.5: 10, 44 Sec. 3.6: 21 Sec. 3.7: 23 Sec. 4.1: 43 (to begin show that there are infinitely many Fibonacci numbers f_n divisible by 5) HW2: Due Wednesday September 19 Sec. 2.1: 1, 12 Sec. 2.3: 14 Sec. 3.1: 20 (use Dirichlet's theorem stated as Theorem 3.3 in Sec. 3.1) Sec. 3.2: 3 Sec. 3.3: 6, 24 Homework 1 Suggested Practice Problems: Sec. 1.2: 4, 6, 7, 10, 16, 17, 22, 24, 27 Sec. 1.3: 4, 7, 8, 9, 16, 20, 24, 32, 33 Sec. 1.4: 7, 14 Sec. 1.5: 16, 31, 36, 49, 55 Sec. 2.1: 8, 11, 12, 14 Sec. 2.3: 1, 10, 13, 14, 15 Sec. 3.1: 10, 17, 20, 29 Sec. 3.2: 10, 25, 27 Sec. 3.3: 2(e), 10, 11, 18, 30 Sec. 3.4: 1, 3, 5, 8, 11, 19, 20, 21, 23 Sec. 3.5: 2, 4(c),(d), 8, 10, 11, 12, 18, 41, 43, 44 Sec. 3.6: 16, 17, 21, 23 Sec. 3.7: 1, 15(a), 11(a), 23, 24 Sec. 4.1: 9, 13, 28, 30, 31, 33, 41, 42, 43 Sec. 4.2: 1(c)(d), 8, 14(d), 16, 18 Sec. 4.3: 4, 5, 6, 7, 15, 16, 19, 22, 23 Sec. 4.4: 1, 2, 3, 9, 10, 11 Sec. 6.1: 1, 9, 14, 16, 17, 19, 29, 41, 52 Sec. 6.2: 2, 6, 16(a) Sec. 6.3: 1, 3, 4, 6, 11, 13, 14, 17, 10 Sec. 7.1: 2, 4, 6, 12, 32, 37-41, 44, 45 Sec. 7.2: 1, 2(b)(c), 3, 12, 22, 23, 40 Sec. 7.3: 1, 3 Sec. 7.4: 1, 10, 17, 18, 21, 27 Sec. 8.1: 3, 5, 7, 10 Sec. 8.3: 1, 5, 6 Sec. 8.4: 1, 3, 4, 5, 8, 13, 14 Sec. 9.1: 2, 4, 8, 9, 11, 12, 14, 19 Sec. 9.2: 1, 6, 7, 9, 12, 16 Sec. 9.3: 2, 8, 14 |
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Course Information
Text: Elementary Number Theory and Its Applications, Kenneth H. Rosen, 6th edition Time of lectures: Monday-Wednesdays 4:00PM - 5:15PM Location of lectures: 103 Alexander Allen Hall o There will be 2 midterms, one final exam, and weekly homeworks. o Midterm 1: Wednesday October 10 o Midterm 2: Wednesday November 14 o Midterms are during the lectures and 1 hour and 15 min. long. o Final grade is 50% final exam, 15% each midterm and 20% (best 10) homeworks. This course is an introduction to number theory and some of its applications: o Mathematical induction, integer representations and operations. o Primes and greatest common divisors, Euclidean algorithm, Fundamental Theorem of Arithmetic, linear Diophantine equations. o Congruences and modular arithmetic, Fermat's and Euler's theorems, Wilson's theorem. o Multiplicative functions such as Euler's phi function, Mobius function and Mobius inversion. o Some applictions in cryptography, RSA, primitive roots, discrete logarithm and index arithmetic. o Quadratic residues and Gauss's quadratic reciprocity.
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Instructor's
Information
Email: kaveh AT pitt.edu Office: Thackeray #424 Office hours: 3:00PM-4:00PM MW or by appointment. You can drop by anytime, I am usually in. Office phone: 412-624-8331 TA for the course is Elise Villella |