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Thu. Sept. 5:
Lecture 1: Natural Numbers
HW
(due Sept. 8, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw1.pdf)
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mathworld
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B. Russell's essay
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Mon. Sept. 9:
Lecture 2: Proof by Induction
HW
(due Sept. 15, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw2.pdf)
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attendance quiz,
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Thu. Sept. 12:
Lecture 3: Fibonacci numbers
HW
(due Sept. 15, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw3.pdf)
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Mon. Sept. 16:
Lecture 4: Representation of integers; Addition and Multiplication
HW
(due Sept. 22, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw4.pdf)
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attendance quiz,
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Thu. Sept. 19:
Lecture 5: Prime numbers and the sieve of Eratosthenes
HW
(due Sept. 22, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw5.pdf)
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Mon. Sept. 23:
Lecture 6: The Fundamental Theorem of Arithmetic
HW
(due Sept. 29, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw6.pdf)
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Thu. Sept. 26
Lecture 7: Greatest Common divisor
HW
(due Sept. 29, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw7.pdf)
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[quiz 1 (on lectures 1-5)]
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quiz 1,
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solutions to quiz 1.
average: 8.87 (out of 10)
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Mon. Sept. 30:
Lecture 8: The Euclidean Algorithm
HW
(due Oct. 6, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw8.pdf)
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Thu. Oct. 3:
Guest Lecturer:
Ms. Aurora Hiveley
Lecture 9: Modular arithmetic
HW
(due Oct. 6, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw9.pdf)
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[quiz 2 (on lectures 6 and 7)]
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quiz 2,
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solutions to quiz 2.
average: 9.75 (out of 10)
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Mon. Oct. 7:
Lecture 10: Linear Congruences
HW
(due Oct. 13, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw10.pdf)
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Thu. Oct. 10:
Lecture 11: The Chinese Remainder Theorem
HW
(due Oct. 13, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw11.pdf)
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[quiz 3 (on lectures 8 and 9)]
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quiz 3,
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solutions to quiz 3.
average: 9.77 (out of 10)
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Mon. Oct. 14: Exam 1 (On lectures 1-10)
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Exam I,
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solutions to Exam I.
average:94.1 (our of 100) (s.d.: 3.1128)
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Thu. Oct. 17:
Lecture 12: Divisibility Rules and Perpetual Calendar
HW
(due Oct. 20, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw12.pdf)
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[quiz 4 (on lectures 10 and 11)]
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quiz 4,
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solutions to quiz 4.
average: 9.85 (out of 10)
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Mon. Oct. 21:
Lecture 13: Wilson's Theorem and Fermat's Little Theorem
HW
(due Oct. 26, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw13.pdf)
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wiki2.
See also pp. 10-11 of
Dr. Z.'s essay .
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Thu. Oct. 24:
Lecture 14: Pseudoprimes and probabilistic primality tests
HW
(due Oct. 26, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw14.pdf)
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[quiz 5 (on lectures 12)]
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quiz 5,
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solutions to quiz 5.
average: 5.57 (out of 10)
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Mon. Oct. 28: Lecture 15:
Lecture 15: Euler's Totient (Phi) function
HW
(due Nov. 3, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw15.pdf)
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Thu. Oct. 31:
Lecture 16: Euler's Theorem and the RSA encrypton algorithm
HW
(due Nov. 3, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw16.pdf)
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[quiz 6 (on lectures 13 and 14)]
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quiz 6,
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solutions to quiz 6.
average: 6.87 (out of 10)
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Mon. Nov. 4:
Lecture 17: The sum and number of divisors
HW
(due Nov. 10, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw17.pdf)
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mathworld
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[original] attendance quiz,
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solutions to the attendance quiz.
[I forgot to bring them to class, so I made a different, but similar attendance quiz]
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Thu. Nov. 7:
Lecture 18: Perfect Numbers and Mersenne Primes
HW
(due Nov. 10, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw18.pdf)
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[quiz 7 (on lectures 15 and 16)]
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quiz 7,
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solutions to quiz 7.
average: 8.125 (out of 10)
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Mon. Nov. 11:
Lecture 19:
The Möbius function and The Möbius inversion formula
HW
(due Nov. 17, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw19.pdf)
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attendance quiz,
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Thu. Nov. 14:
Lecture 20:
Quadratic residues and the law of Quadratic Reciprocity
HW
(due Nov. 17, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw20.pdf)
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mathworld
[quiz 8 (on lectures 17 and 18)]
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quiz 8,
and here are the
solutions to quiz 8.
Here is the attendance quiz,
and here are the
solutions to the attendance quiz.
[Note: The above attendance quiz was made up in class, since I forgot to bring them.
Here is the original attendance quiz,
and
here is the solutions to the original attendance quiz]
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Mon. Nov. 18:
Lecture 21: Integer Partitions I
HW
(due Nov. 24, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw21pdf)
wiki
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Thu. Nov. 21:
Lecture 22: Integer Partitions II
HW
(due Nov. 24, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw22.pdf)
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[quiz 9 (on lectures 19 and 20)]
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quiz 9,
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solutions to quiz 9.
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attendance quiz,
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Mon. Nov. 25: Review
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Tue. Nov. 26:
Exam 2 (On lectures 1-22, with an emphasis on lectures 11-22)
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Mon. Dec. 2:
Lecture 23:
Integer Partitions III: The Pentagonal Number Theorem, Recurrence for p(n)
HW
(due Dec. 8, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw23.pdf)
wiki
Bressoud-Zeilberger gem
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Thu. Dec. 5:
Lecture 24:
Continued Fractions
HW
(due Dec. 8, 8:00pm. Email ShaloshBEkhad@gmail.com, with an attachment LastFirstHw24.pdf)
wiki
Benjamin-Zeilberger gem (optional reading)
[quiz 10 (on lectures 21 and 22)]
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Mon. Dec. 9: REVIEW