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Welcome!
Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,
CHECK AT LEAST ONCE A WEEK!!
COURSE PAGE WITH SYLLABUS, GRADING SCHEME ETC

UPDATE PAGE FROM SPRING 2026 WITH NOTES AND TEST SOLUTIONS
Use this to refer to what we did last time. We will follow the same schedule and topics.
I may also add a few and modify some things as we go along.

Textbook:
Analysis with Introduction to Proofs by Stephen Lay, 4th edition, Prentice Hall.



Started Aug 11, 2026.


Saturday, 8-15-26
In our first class we will introduce ourselves, talk about how the course will be structured and provide important information about things you need to pay attention to, throughout the semester.
In remaining time we will discuss the emerging field of AI generated math.

Some questions for you:
What does AI mean?
How does it work?
What are some of the things it can do?
What does it mean for society?

Try to listen to these two talks by Terry Tao, one of the best mathematicians around.
Talk at the International Conference of Mathematicians that just concluded in Philadelphia.
Terry Tao's talk on machine learning and mathematical proofs.


Tuesday, 8-11-26.
You can see what we did in the final exams and in our first class of last semester.
Final exam problems.
Final exam solutions.

Notes from first class of 2019.

We saw how to prove Pythagorean theorem using geometry.
Outline of the proof given by two high school students in New Orleans using trigonometry.

Fun question to think about, before next class:
We saw that the moon rotates exactly one time around its own axis as it does one full rotation around the earth.
Note that, as it goes around the earth, it is facing the same way.
Suppose it also rotates around its own axis exactly once at the same time. So every part of the moon will be facing the earth at some point during a single rotation of the moon around the earth.
This time how many rotations around its axis in one rotation around the earth?

Now imagine two circular disks (maybe coins) touching each other on a flat surface.
If one os smaller and of radius 1 unit, and the other is of radius 2 units, how many times does the smaller disk rotate about its own axis as you roll it around the larger disk, always keeping them in contact?