MATH-UA 325 Analysis 1 Fall 2023

What is this Course About?

It is an introduction to real analysis. It is also an introduction to writing rigorous (i.e., logically precise) mathematical proofs. The course is very challenging for many students, because proofs in analysis can be quite convoluted.

Special Accommodations

If you are student with a disability who needs special accommodations, please contact New York University’s Moses Center for Students with Disabilities (CSD) at 212-998-4980 or mosescsd@nyu.edu. You must be registered with CSD to receive accommodations. Information about the Moses Center can be found at www.nyu.edu/csd. The Moses Center is located at 726 Broadway on the 2nd floor.

If you think it's possible that you might have a learning disability, please get tested. See Diagnosing A Learning Disability In College for more information.

Calendar (subject to change)

Important Websites

• Gradescope: For homework submission and grades (See Homework below)
• Ed Discussion: For online discussions (See Getting Help below)
• Overleaf (optional): For preparation of homework solutions using LaTeX.

Textbook

Jiří Lebl, Basic Analysis: Introduction to Real Analysis

Other Sources

• Other textbooks
  • Stephen Abbott, Understanding Analysis
  • Nets Katz, Calculus for Cranks
  • Charles Pugh, Real Mathematical Analysis
  • Terence Tao, Analysis I
• You are allowed to consult other sources, including but not limited to books, whatever you can find on the web, and people.
• But remember that you need to focus on learning how to solve new problems you haven't seen before.
• Learning how to solve specific problems is not enough.

Getting Help

• Remember: The most important skill for doing well on exams is knowing how to figure out how to solve a problem you have not seen before. Knowing only how to do the assigned homework problems is not enough.
• Work together with classmates. But be careful! If you simply copy someone else's answers without struggling through the problem yourself, you will not be ready for the exams. Get help from other students but, when preparing final version of your solutions, do it alone.
• Post questions, no matter how vague or dumb, to Ed Discussion. You are allowed to do this anonymously. Please do not email math questions to me. All questions should be posted to Ed Discussion, so everyone can see the questions.
• You are also encouraged to post answers, even partial ones, to questions asked on Ed Discussion. It is a good way to get feedback on your understanding of the material.
• Ask me during office hours. If you cannot make it during the scheduled times, please email me to make an appointment.

Other questions

Homework

• There will be a weekly homework assignment.
• The assignment will be made available as a PDF on Gradescope.
  • Please email me if you need a Gradescope account.
• You will submit your solutions using Gradescope as follows:
  • Write up your solutions clearly, legibly, dark enough, and large enough so that a half-blind professor can read it all easily
    • The grader will be instructed to give a zero score for any solution they are unable to read EASILY.
    • If I consider a regrade request and am unable to read the solution EASILY, I will deny the request.
  • The solution to each part of a problem should start on a new page.
  • Create a PDF of your solutions and upload to Gradescope as a variable length assignment.
• Your graded solutions will be returned to you via Gradescope.
• You may submit a regrade request for a specific problem via Gradescope.

Course Grade Factors (subject to change)

• Homework (30%)
• Midterm (30%)
• Final (40%)
• Tweaks