Exams

Final exam

Date:	Thursday, August 5, 2010
Time:	9 am--11:30 am
Rooms:	PAC 4,5,6

Allowed materials

You may use a non-programmable, non-graphing calculator on the exam. You may not use the course text, your course notes, or any other written materials.

Please bring your WatCard to the exam for identification.

Syllabus

The exam will cover all of the material covered in class, although the emphasis is on the material from the Fermat Little theorem onwards (the "new material"). Roughly a third of the final exam is on material already covered in the midterm, and two-thirds on the new material. Be aware that a lot of the new material builds upon the old. For example, induction and recursion are used throughout the course; RSA uses the Euclidean algorithm for GCDs, the recursive powering algorithm, and modular arithmetic.

The relevant sections of the text book and supplementary lecture notes are listed on the lecture schedule. The lectures are the primary source of material for the course. The presentation in the lectures is sometimes different from that in the text, and not all of the material in the text is relevant. You are expected to be familiar with every definition, result, and algorithm we covered in class. In particular, you will be asked to prove a least one of the following:

• Proposition 2.1.3
• Proposition 2.3.3
• Illustration 7 in Section 1.7
• Proposition 3.1.3
• Theorem 3.1.7
• Lemma 6.2.10
• Lemma 6.2.13
• Lemma 6.4.11
• Theorem 10.1.7
• Theorem 10.2.4
• Theorem 10.3.4

When referring to results from class or the text book, give a description of the result rather than referring to a specific number. For example, to invoke Proposition 2.1.2(i), you could write “by the proposition saying that if a|b and b|c, then a|c, ...”. For major results with common names (such as the Division Algorithm, Euclidean Algorithm, or the Bezout Lemma), it is fine to refer to the result by name.

Sample exams/questions

Advice on exam preparation: review the notes you take during lectures, the text, and the supplementary notes posted at this page. Ensure that you understand how to solve the questions on the homework and the quizzes; refer to the solutions if need be. Try the suggested problems posted on the homework page.

For more detailed advice on exam preparation, see the MathSoc page.

Here are the exams from the last few offerings of the course (some with solutions), along with the questions relevant to this term:

• Winter 10 midterm: Questions 1 to 7.
• Winter 10 final: Questions 1 to 5.
• Spring 09 midterm: Questions 3, 4, 6, 7, 8, 9. (Note: we may prove 6(a) using simple properties of GCDs; the Good Characterization Theorem is not needed)
• Spring 09 final: Questions 1, 2, 3, 6, 7, 8, 9(a), 9(c), 10.
• Spring 08 midterm: Questions 1.3, 2, 3, 5, 6.
• Spring 08 final: Questions 1, 2, 4, 5, 6, 8.

You can find other recent past exams at the MathSoc Exam Bank. The course content this term is different from that in the previous terms, so not all questions are relevant to the midterm exam, and you may not see questions pertaining to new topics (e.g., recursion, Eulerian graphs). Some of the relevant questions are as follows:

• Spring 2007 midterm: 1(a), 2(a-c), 6(b,c,d,f), 7.
• Spring 2007 quiz 1: 1(a), 2, 3, 5
• Spring 2007 quiz 2: 1, 2, 3, 4.
• Spring 2006 midterm: 3, 4(a,c), 5, 6, 7, 9
• Spring 2004 midterm: 1 (find only one pair x,y), 2, 3, 5(d), 9 (find the remainder of 8³⁴¹ when it is divided by 9)
• Winter 2004 midterm: 2, 3 (find only one pair x,y), 5, 6, 7
• Winter 2004 final: 1, 3, 5 (RSA), 6, 7, 9, 10, 11(b), 12(a).

Review/extra help

The instructors have review sessions the day before the exam:

Koray Karabina: Wednesday, August 4, 2010, 4:00 to 6:00 pm, in MC 4059.
Ashwin Nayak: Wednesday, August 4, 2010, 10:30 am to 12:30 pm, in MC 4059.

Please bring any questions you may have from the lectures, text book, home work assignments, quizzes, or suggested problems to the session; it will be driven entirely by the students.

The TAs have the following office hours:

Nicolas L.: Tuesday, Aug 3, 4--5 pm.
Nina Z.: Tuesday, Aug 3, 4--5 pm.
Drew L.: Wednesday, Aug 4, 8:30--9:30 am.
Vladimir S.: Wednesday, Aug 4, 2--3 pm.
Isabel U.-S.: Wednesday, Aug 4, 3--4 pm.

Midterm

The exam has passed; here are the solutions: [ pdf ]

Date:	Wednesday, June 16, 2010
Time:	7 pm--9 pm
Rooms:	Please go to one of the following rooms according to your last name, and lecture section

(Section) Instructor	Last name starts with	Exam room
(1) Koray Karabina	A–Pi	RCH 301
(1) Koray Karabina	Pr–Z	RCH 305
(2) Ashwin Nayak	A–Lo	RCH 105
(2) Ashwin Nayak	Lu–Z	RCH 110

Allowed materials

You may use a non-programmable, non-graphing calculator on the exam. You may not use the course text, your course notes, or any other written materials.

Please bring your WatCard to the exam for identification.

Syllabus

The exam will cover all of the material covered in class through modular arithmetic (excluding the Fermat Little Theorem). The relevant sections of the text and supplementary lecture notes are listed on the lecture schedule. The lectures are the primary source of material for the course. The presentation in the lectures is sometimes different from that in the text, and not all of the material in the text is relevant. You are expected to be familiar with every definition, result, and algorithm we covered in class. In particular, you will be asked to prove a least one of the following:

• Proposition 2.1.3
• Proposition 2.3.3
• Illustration 7 in Section 1.7
• Proposition 3.1.3
• Theorem 3.1.7

When referring to results from class or the text, give a description of the result rather than referring to a specific number. For example, to invoke Proposition 2.1.2(i), you could write “by the proposition saying that if a|b and b|c, then a|c, ...”. For major results with common names (such as the Division Algorithm, Euclidean Algorithm, or the Bezout Lemma), it is fine to refer to the result by name.

Sample midterms/questions

Advice on exam preparation: review the notes you take during lectures, the text, and the supplementary notes posted at this page. Ensure that you understand how to solve the questions on the homework and the quizzes; refer to the solutions if need be. Try the suggested problems posted on the homework page.

For more detailed advice on exam preparation, see the MathSoc page.

Here are the midterms from the last few offerings of the course (some with solutions), along with the questions relevant to this term:

• Winter 10: Questions 1 to 6.
• Spring 09: Questions 3, 4, 6, 7, 8, 9. (Note: we may prove 6(a) using simple properties of GCDs; the Good Characterization Theorem is not needed)
• Spring 08: Questions 1.1, 2, 3, 5, 6.

You can find other recent past exams at the MathSoc Exam Bank. The course content this term is different from that in the previous terms, so not all questions are relevant to the midterm exam, and you may not see questions pertaining to new topics (e.g., recursion, recurrence relations). Some of the relevant questions are as follows:

• Spring 2007 midterm: 1(a), 2(a-c), 6(b,c,d), 7.
• Spring 2007 quiz 1: 1(a), 2, 3, 5
• Spring 2006 midterm: 3, 4(a), 5, 6, 7, 9
• Spring 2004 midterm: 1 (find only one pair x,y), 2, 3, 5(d), 9 (find the remainder of 8³⁴¹ when it is divided by 9)
• Winter 2004 midterm: 2, 3 (find only one pair x,y), 5(a,c,d), 6, 7

Review/extra help

There is no home work due on Monday, June 14, and no quiz. The tutorial is reserved for a review and to answer any questions you may have. The instructors have extra office hours, in addition to the regular ones:

Koray Karabina: Wednesday, June 16, 12:30--2:30 pm.
Ashwin Nayak: Tuesday, June 15, 4:30--6:30 pm.