Math 325: Real Analysis I

Spring 2025

Syllabus

Spring 2025 Office Hours: Monday 2:30–3:30 PM, Tuesday 3:30–4:20 PM, Friday 3–4 PM

Daily Work

How to Read Mathematics by Shai Simonson and Fernando Gouvea
Date AssignedReading/TopicAssignment
Monday, January 13, 2025Introduction to analysis Daily Work 1 ($\operatorname{\LaTeX}$ file)
Wednesday, January 15, 2025Triangle inequality Daily Work 2 ($\operatorname{\LaTeX}$ file)
Friday, January 17, 2025Sets and functions Daily Work 3 ($\operatorname{\LaTeX}$ file)
Wednesday, January 22, 2025Supremums and infimums Daily Work 4 ($\operatorname{\LaTeX}$ file)
Friday, January 24, 2025Supremums and Infimums Daily Work 5 ($\operatorname{\LaTeX}$ file)
Monday, January 27, 2025AoC and friends Daily Work 6 ($\operatorname{\LaTeX}$ file)
Wednesday, January 29, 2025Cardinality Daily Work 7 ($\operatorname{\LaTeX}$ file)
Friday, January 31, 2025Cardinality Daily Work 8 ($\operatorname{\LaTeX}$ file)
Monday, February 3, 2025Cantor's Diagonalization Daily Work 9 ($\operatorname{\LaTeX}$ file)
Wednesday, February 5, 2025Cantor's Diagonalization Daily Work 10 ($\operatorname{\LaTeX}$ file)
Friday, February 7, 2025Sequence Convergence Daily Work 11 ($\operatorname{\LaTeX}$ file)
Monday, February 10, 2025Algebraic and Order Limit Theorems Daily Work 12 ($\operatorname{\LaTeX}$ file)
Wednesday, February 12, 2025MCT Daily Work 13 ($\operatorname{\LaTeX}$ file)
Friday, February 14, 2025MCT Daily Work 14 ($\operatorname{\LaTeX}$ file)
Monday, February 17, 2025Cauchy Condensation Test Daily Work 15 ($\operatorname{\LaTeX}$ file)
Wednesday, February 19, 2025Subsequences and the BWT Daily Work 16 ($\operatorname{\LaTeX}$ file)
Friday, February 21, 2025Cauchy sequences Daily Work 17 ($\operatorname{\LaTeX}$ file)
Monday, February 24, 2025series Daily Work 18 ($\operatorname{\LaTeX}$ file)
Wednesday, February 26, 2025series Daily Work 19 ($\operatorname{\LaTeX}$ file)
Friday, February 28, 2025series Daily Work 20 ($\operatorname{\LaTeX}$ file)
Monday, March 10, 2025open and closed sets Daily Work 21 ($\operatorname{\LaTeX}$ file)
Wenesday, March 12, 2025limit points, isolated points, closure, complements Daily Work 22 ($\operatorname{\LaTeX}$ file)
Friday, March 14, 2025limit points, isolated points, closure, complements Daily Work 23 ($\operatorname{\LaTeX}$ file)
Monday, March 17, 2025limit points, isolated points, closure, complements Daily Work 24 ($\operatorname{\LaTeX}$ file)
Friday, March 21, 2025compactness Daily Work 25 ($\operatorname{\LaTeX}$ file)
Monday, March 24, 2025compactness Daily Work 26 ($\operatorname{\LaTeX}$ file)
Wednesday, March 26, 2025functional limits Daily Work 27 ($\operatorname{\LaTeX}$ file)
Monday, March 30, 2025functional limits Daily Work 28 ($\operatorname{\LaTeX}$ file)
Wednesday, April 2, 2025functional limits Daily Work 29 ($\operatorname{\LaTeX}$ file)
Friday, April 4, 2025continuity Daily Work 30 ($\operatorname{\LaTeX}$ file)
Monday, April 7, 2025continuity Daily Work 31 ($\operatorname{\LaTeX}$ file)
Wednesday, April 9, 2025uniform continuity Daily Work 32 ($\operatorname{\LaTeX}$ file)
Friday, April 11, 2025uniform continuity Daily Work 33 ($\operatorname{\LaTeX}$ file)
Monday, April 14, 2025IVT Daily Work 34 ($\operatorname{\LaTeX}$ file)
Wednesday, April 16, 2025IVT Daily Work 35 ($\operatorname{\LaTeX}$ file)
Wednesday, April 23, 2025Derivatives Daily Work 36 ($\operatorname{\LaTeX}$ file)
Friday, April 25, 2025MVT and friends Daily Work 37 ($\operatorname{\LaTeX}$ file)
Monday, April 28, 2025integrability Daily Work 38 ($\operatorname{\LaTeX}$ file)
Wednesday, April 30, 2025integrability Daily Work 39 ($\operatorname{\LaTeX}$ file)

Quizzes

Friday, March 14
Quiz and ChapterDate
Chapter 1 Quiz Wednesday, February 12
Chapter 2 Quiz
Chapter 4 QuizWednesday, April 16
Chapter 5 Quiz
Chapter 7 Quiz

Celebrations of Learning

Celebration of Learning Due Date
Midterm Celebration of Learning: Chapters 1–3 Friday, March 28 (in class portion)
Cumulative Final Celebration of Learning