Overview
In this course we will begin a study of real analysis, including basic properties if the real numbers, sequences and series, various notions of convergence, differentiation and integration.Instructors
Dagan KarpOffice hours: Tue 4:005:00 pm, and Thu 3:004:00 pm by appointment, and open door.
Office Location: Shanahan 3414
Tutors and Graders
Emily Fischer, Alexander Gruver and Ben Lowenstein are tutoring and grading for this course. You should talk to them frequently and take advantage of their expertise! Tutoring hours are:Tuesday: 79 pm
Textbook
The official text for this course is Principles of Mathematical Analysis, by Walter Rudin.Grades
There will be two midterms, one final exam and weekly homework. Each will count one fifth of your grade. The remaining fifth is the maximum of these four items.Homework
Written homework will be due in class each Wednesday, and is posted below. Late homework may not be accepted. Each student's lowest homework score will be dropped. Please consult the HMC mathematics homework format guidelines for helpful tips on homework submission and formatting.Rewrites
Students have the opportunity to turn in a rewritten copy of the first four homeworks for a revised grade. Details can be found on the Math 131 Rewrite Policy.Exams
There will be three exams. The first exam will be inclass on Monday, February 24. The second exam will be takehome, out Wed March 26 and due Mon March 31. The third exam will be either takehome or inclass, but will be due at 2pm on Wednesday, May 14.LaTeX
Students should feel free to use LaTeX for homework, but this isn't required.Disabilities
Students who need disabilityrelated accommodations are encouraged to discuss this with the instructor as soon as possible.Honor Code
Though cooperation on homework assignments is encouraged, students are expected to write up their own solutions individually. That is, no copying. Comprehension is the goal, so even with cooperation, you should understand solutions well enough to write them up yourself. It is appropriate to acknowledge the assistance of others; if you work with others on a homework question, please write their names in the margin. Tests are to be done individually. You are encouraged to discuss your paper with other students. The HMC Honor Code applies in all matters of conduct concerning this course.LaTeX Lecture Notes
These lecture notes are generously provided by Julius Elinson. Beware they may contain typo's and mistakes coming directly from the
blackboard!
Lecture 2 PDF, TEX
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iPad Lecture Notes
These lecture notes are generously provided by Hannah Rose. As always, beware of typos!Lecture 1: Construction of Q, introduction to Fields, example of an irrational number.
Lecture 2: Suprema, Infima and Dedekind Cuts
Lecture 3: Extensions of R, Definition of C, and Introduction to Countable Sets
Lecture 4: Countable and Uncountable Sets
Lecture 5: Introduction to Metric Spaces, Neighborhoods, Interior Points, Limit Points
Lecture 6: Open and Closed Sets, Closure and Interior, Definition of a Topology
Lecture 7: Subspace Topology, Compact Sets
Lecture 8: HeineBorel and BalzanoWeierstrass
Lecture 9: Connected Sets, Introduction to Sequences
Lecture 10:Basic properties of sequences, Cauchy sequences
Lecture 11: Subsequences, upper and lower limits, complete metric spaces, the completion of a metric space
Lecture 12: Properties of upper and lower limits, special sequences, definition of infinite series as a sequence of partial sums
Lecture 13: Infinite Series, Cauchy Criterion for Series, Divergence Test, Comparison Test, Geometric Series, the number e
Lecture 14: pserier, Ratio Test, Root Test, Rearrangements, Alternating Series
Lecture 15: Limits and Continuity
Lecture 16: Continuity Continued, Topological Characterization, Continuous Images and Compact and Connected Sets
Lecture 17: Continuous Images of Connected Sets, Continuous Inverses of Bijections on Compact Sets, Intermediate Value Theorem, Uniform Continuity
Lecture 18: Lebesgue Number Lemma, Discontinuities of the First and Second Kind, Pointwise Limits of Sequences and Series of Functions
Lecture 19: Uniform Convergence of a Sequence of Functions, Introduction to Differentiability
Lecture 20: Derivatives Continued, Mean Value Theorem
YouTube Lectures
Francis Su delivered these lectures in 2010. My lectures will be very different, but you may find these valuable for review, or, better yet, watch them before the class lecture, and then during class you can ask questions!Lecture 1: Constructing the rational numbers
Lecture 2: Properties of Q
Lecture 3: Construction of R
Lecture 4: The Least Upper Bound Property
Lecture 5: Complex Numbers
Lecture 6: The Principle of Induction
Lecture 7: Countable and Uncountable Sets
Lecture 8: Cantor Diagonalization, Metric Spaces
Lecture 9: Limit Points
Lecture 10: Relationship b/t open and closed sets
Lecture 11: Compact Sets
Lecture 12: Relationship b/t compact, closed sets
Lecture 13: Compactness, HeineBorel Theorem
Lecture 14: Connected Sets, Cantor Sets
Lecture 15: Convergence of Sequences
Lecture 16: Subsequences, Cauchy Sequences
Lecture 17: Complete Spaces
Lecture 18: Series
Lecture 19: Series Convergence Tests
Lecture 20: Functions  Limits and Continuity
Lecture 21: Continuous Functions
Lecture 22: Uniform Continuity
Lecture 23: Discontinuous Functions
Lecture 24: The Derivative, Mean Value Theorem
Lecture 25: Taylor's Theorem
Lecture 26: Ordinal Numbers, Transfinite Induction
Homework Assignments
Homeworks, due Thursdays in class
All HW's refer Rudin's Principles of Mathematical Analysis. 

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Exam 3. 
Possible upcoming homeworksBelow this line, all homeworks are TENTATIVE. This means they are likely to be assigned, but there is no guarantee that they will until you see them moved to the box ABOVE. I am putting them here in case you want to work ahead! 