Math 308, Fall 2016, Van Gool

Mathematical Bridge, Queens College, Cambridge

Bridge to Advanced Mathematics

Math 30800, Section R, Fall 2016

Math 30800-R meets on Tuesday and Thursday, 3:30-4:45 PM in NAC 6/111
First class: Aug 25. Last class: Dec 8. No class on Oct 4, Oct 6, Oct 11, Nov 24. Friday class on Oct 14.
Final exam: Dec 20.

Textbooks

CPZ = Mathematical Proofs: A Transition to Advanced Mathematics, G. Chartrand, A. D. Polimeni, P. Zhang, 3rd edition, Pearson.
R = Elementary Analysis: The Theory of Calculus, K. A. Ross, 2nd edition, Springer.

Calendar

Note: This calendar is tentative, it is being updated as the term progresses.

Date	Class contents	Read before next class	Homework
Th 8/25	Course Information and Learning Outcomes, CPZ 1.1-1.3	CPZ Ch. 0 & 1	HW #1
Tu 8/30	CPZ 1.4-1.5	CPZ Ch. 2
Th 9/1	CPZ 1.6, 2.1-2.5		HW #2
Tu 9/6	CPZ 2.6-2.9	CPZ Ch. 3
Th 9/8	CPZ 2.10-2.11, Ch. 3, 4.1		HW #3
Tu 9/13	CPZ Ch. 3, 4.2
Th 9/15	CPZ 4.3-4.6		HW #4
Tu 9/20	Review		Review
Th 9/22	MIDTERM EXAM #1	CPZ Ch. 5
Tu 9/27	CPZ 5.1-5.3	CPZ Ch. 6
Th 9/29	CPZ 5.4-5.5, 6.1		HW #5
Th 10/13	CPZ 6.2
Fr 10/14	CPZ 6.3-6.4	CPZ Ch. 7	HW #6
Tu 10/18	CPZ Ch. 7.1-7.2	CPZ Ch. 8
Th 10/20	CPZ Ch. 7.3, 8.1-8.3		HW #7
Tu 10/25	CPZ Ch. 8.3-8.4
Th 10/27	CPZ Ch. 8.4-8.6	CPZ Ch. 9	HW #8
Tu 11/1	Review
Th 11/3	Review		Review
Tu 11/8	MIDTERM EXAM #2
Th 11/10	CPZ Ch. 9.1-9.3
Tu 11/15	CPZ Ch. 9.3-9.6	CPZ Ch. 10	HW #9
Th 11/17	CPZ Ch. 9.7, Ch. 10
Tu 11/22	CPZ Ch. 10	R Ch. 1	HW #10
Tu 11/29	R Ch. 1, §2
Th 12/1	R Ch. 1, §4-5, Ex. 2.7(a)		HW #11
Tu 12/6	R Ch. 1, §3
Th 12/8	R Ch. 1, Review
Tu 12/20	FINAL EXAM

Homework

Writing proofs, one of the main goals of this course, can only be learned by doing it yourself. Homework is therefore crucial for success in this class.
Homework will be assigned weekly (approximately, see calendar), is due at the beginning of class and may be handed in either on paper or to the instructor via email.
The instructor will select a number of exercises from each homework set to grade and provide feedback on.
Discussing homework problems with others is useful, but copying another person's solutions is not.
You should indicate who you worked with on which problems.
You should write your final solutions yourself.
If you use any outside sources (e.g., the internet), you should say so and give the link or reference.

	Exercises	Due Date
HW #1	CPZ 1.1: 3, 4, 7, 9. 1.2: 12, 14, 16, 21. 1.3: 22, 26, 30, 32.	Tu 8/30
HW #2	CPZ Ch. 1: 37, 40, 42, 45, 46, 50, 53, 54, 59, 62. Ch. 2: 6, 13, 16, 17, 20, 24, 30, 32.	Tu 9/6
HW #3	CPZ Ch. 2: 36, 42, 47, 48, 49, 51, 54, 58, 60, 68, 74, 78 Ch. 3: 8, 16, 18.	Tu 9/13
HW #4	CPZ Ch. 3: 20, 21, 28, 31. Ch. 4: 1, 6, 10, 15, 27, 34, 40, 42, 50, 56, 65.	Tu 9/20
HW #5	HW #5 problems	Th 10/13
HW #6	HW #6 problems	Tu 10/18
HW #7	HW #7 problems	Tu 10/25
HW #8	HW #8 problems	Tu 11/1
HW #9	HW #9 problems	Tu 11/22
HW #10	HW #10 problems	Tu 11/29
HW #11	HW #11 problems	Tu 12/6

Exams and Grading

Your class average is determined by

Two midterm exams (2 x 20% = 40%)
Homework (20%)
Final (40%)

It is every student's own responsibility to attend every class and not be late.

If you need to miss an in-class exam, notify the instructor by email before the start of the exam.
If you will need to be absent for a religious holiday, notify the instructor by email before September 6th.

Midterm #1

The first midterm exam will take place on Thursday September 22, 2016 from 3:30-4:45 in NAC 6/111.
The midterm covers all the lectures up until this point, which corresponds to Chapters 1-4 of CPZ.
To get an idea of the level and style of the questions on the midterm, the homework gives a good indication.
The following previous homework exercises are particularly useful to review:
Ch. 1: 3, 14, 30, 40, 42, 46, 53, 59.
Ch. 2: 13, 17, 24, 32,42, 48, 51, 54, 60, 68, 78.
Ch. 3: 18, 21, 31.
Ch. 4: 1, 10, 27, 34, 42, 56, 65.
The following additional exercises are useful for extra practice:
Ch. 1: 69, 70, 71, 76, 85.
Ch. 2: 85, 88, 89, 91, 93, 97, 100.
Ch. 3: 46, 50, 53, 56, 62, 64, 67.
Ch. 4: 71, 73, 75, 79, 81, 84, 94.
You should also know the definitions and theorems stated in the lectures. You should be able to prove the results that were proved in the lectures.
Midterm #1, with solutions

Midterm #2

The second midterm exam will take place on Tuesday November 8, 2016 from 3:30-4:45 in NAC 6/111.
The midterm covers the lectures since the first midterm (9/27) up until this point, which corresponds to Chapters 5-8 of CPZ.
To get an idea of the level and style of the questions on the midterm, the homework gives a good indication.
The following additional exercises from CPZ are useful for extra practice:
Ch. 5: 3, 11, 16, 27, 37, 44, 45, 51.
Ch. 6: 5, 9, 15, 18, 24, 31, 35, 38, 41, 44, 45.
Ch. 7: 5, 7, 10, 14, 17, 20, 27, 29, 30, 35, 40, 47, 48, 66, 72, 77.
Ch. 8: 7, 11, 18, 23, 30, 33, 38, 44, 49, 56, 58, 59.
You should also know the definitions and theorems stated in the lectures. You should be able to prove the results that were proved in the lectures.
Midterm #2, with solutions

Final Exam

The final exam will take place on Tuesday December 20, 2016 from 3:30-5:45 in NAC 6/111.
The final exam covers all of the lectures, which corresponds to Chapters 1-10 of CPZ and Chapter 1, §2-5 of Ross.
To get an idea of the level and style of the questions on the final exam, the homework and the two midterm exams give a good indication.
The following additional exercises from CPZ are useful for extra practice:
Ch. 1: 69, 70, 71, 76, 85.
Ch. 2: 85, 88, 89, 91, 93, 97, 100.
Ch. 3: 46, 50, 53, 56, 62, 64, 67.
Ch. 4: 71, 73, 75, 79, 81, 84, 94.
Ch. 5: 3, 11, 16, 27, 37, 44, 45, 51.
Ch. 6: 5, 9, 15, 18, 24, 31, 35, 38, 41, 44, 45.
Ch. 7: 5, 7, 10, 14, 17, 20, 27, 29, 30, 35, 40, 47, 48, 66, 72, 77.
Ch. 8: 7, 11, 18, 23, 30, 33, 38, 44, 49, 56, 58, 59.
Ch. 9: 2, 6, 12, 20, 24, 28, 32, 38, 47, 49, 53, 56, 60.
Ch. 10: 1, 3, 7, 12, 22, 29.

and from Ross:
§2: 1, 2, 3, 7, 8.
§3: 3, 4, 5, 6.
§4: 1, 2, 3, 4.
§5: 1, 2, 3.
You should also know the definitions and theorems stated in the lectures. You should be able to prove the results that were proved in the lectures.