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Class
Schedule
TR 10:10-11:25, 224 Malott Hall
Lecturer
Robert
Connelly, 433 Malott Hall, (607) 255-4301, connelly@math.cornell.edu
Office hours: Monday 3-4, Friday 2-3; 433
Malott Hall
Teaching
Assistant
Michael
O'Connor
Office hours: Wednesday 2-4; 218 Malott Hall
Text
How to Read and Do Proofs by Daniel Solow
(recommended).
Some course notes and definitions.
- Glossary
- Symbolic
Logic: Propositional Calculus
- Symbolic
Logic: Predicate Calculus
- A quick discussion of equivalence
relations from Halmos's "Naive Set Theory", which is on reserve in
the Math Library.
- Here is some advice by
George Polya on how to solve problems and prove things.
- Here is a good
discussion of infinite cardinals in Halmos's book above. Two
copies of this book are on reserve in the Mathematics Library.
- A CD for the book "An interactive introduction to
Mathematical Analysis" by Jonathan Lewin is on reserve in the
Mathematics Library. Part I gives
good advice for learning how to do proofs. We will have some
exercises from this book.
- Here
is more information about the creation/definition of the natural
numbers
as discussed in class.
- Here
is a discussion
of the creation/definition of the integers.
- Here is
a discussion of the creation/definition of the rationals.
- Here
is a discussion of the creation/definition of the real numbers.
- Here
are
things about cardinal numbers.
- Here are some definitions and
theorems about cardinality to help with the homework.
- Here are some problems
for practice for the Prelim on March 13.
- Here are solutions to
the midterm Prelim. The median score was 69 out of a possible 100.
- Here is a collection of
sample questions for the Final exam. Enjoy.
Course Information
We will have regular weekly homework due every
Tuesday, at least one in-class Prelim, and a Final Exam.
We had an in-class
preliminary exam on logic, cardinal numbers, and induction on Thursday,
March 13.
The Final Exam will be
Tuesday, 13-MAY, from 7:00 PM to 9:30 PM in Rockefeller 104.
It will cover all the material in the course with a bit more
emphasis on the material since the mid-term prelim.
The last class on May 1 will be a review.
Please have
questions ready.
Homework Assignments
- Read Chapter 1 in Solow, and do Exercises 1.1, 1.2, 1.4,
1.8. Prove that any projective plane has at least 7 points.
(Use no more
than one page, typewritten, clearly and succinctly presented.)
Find the
simplest proof of Pythagoras's Theorem you can find. Due Tuesday,
January 29, 2008, in class. Solutions.
- Read Chapter 2 in Solow, and Halmos's chapter on
equivalence relations. These exercises
are due February 5, 2008 in class.
This involves a discussion of equivalence relations. Solutions.
- Read Chapter 2 and Chapter 3 in Lewin's book. Do
exercises 3, Section 2.1.5, exercise 3 in Section 2.3.8, exercise 2 in
3.6.6, exercise 4 in Section 3.7.3, exercise 7 in Section 3.8.4,
exercise 9 in Section 4.3.15. Due February 12 in
class. Solutions.
- Read Chapters on the Schröder-Bernstein Theorem and
countable sets in Halmos's book. (CORRECTION)
These
exercises are due February 26, in class. THE EXERCISES HERE ARE CORRECTED from the earlier
version. Solutions. Note the
delay. We will have a short quiz (not graded but collected) in
class on Thursday, February 22. It will cover cardinal numbers.
- We will have a short
quiz (not graded but collected) in class on
cardinal numbers on February 28.
- Read Chapter 11 in Solow's book on mathematical induction.
Here are some problems on our
discussion of the Schröder-Bernstein Theorem and cardinal numbers
as well as induction. Due in class in class Thursday,
March 6. Solutions.
- We will have a short
quiz that will be graded
in the last 20 minutes of class covering mathematical induction on Thursday, March 6.
- Read Appendix C.1 in Solow and do exercises C.2, C.4, and
C.5. Which positive multiples of 5 pounds are NOT possible with
garbage
tags of denominations of 20 pounds and 35 pounds? (Hint: If you
know that
enough cosecutive multiples of 5 ARE positive combinations of 20 and
35,
then all further multiples are positive combinations of 20 and
35. More
hints in class. This problem can be handed in on Thursday.)
Due April 1
(no fooling).Solutions
- There will be a short
quiz that will be graded
in the last 20 minutes of class covering number theory and a little bit
of Appendix D.1 on Thursday, April 3.
- Read Appendix D in Solow and do exercises D.3, D.4.
Due
April 8. (D.9, D11, D12 are due next week.) Solutions.
- There will be a short
quiz that will be graded
in the last 20 minutes of class covering Appendix D.1 and D.2 and glb's
and lub's on Thursday, April 10.
- Do Exercises D.8, D.9, D.11, D.12 in Solow. Due April
15.Solutions
- Do the three problems here.
Due April 22. Solutions. There will be a short quiz covering open sets
and continuity that will be graded
in the last 20 minutes of class on Tuesday, April 22.
- Do the Exercises here.
Due
April 29 in class. You can read about the fractal dimension of
sets with
lots of examples here.Solutions
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