Embedded Files
Class Info
Class Info
Class: Math 3137 - Real and Complex Analysis 1
Lecture Meetings: M/W/F, 9:00 - 9:50 AM on Zoom.
Recitation Meeting: W, 8:00 - 8:50 AM.
Instructor: Zach Bailey
Email: zbailey@temple.edu
Office: My House
Professor's Office Hours: T/Th, 1:30 - 2:30 PM, Wed 10:00 - 11:00 AM, and by appointment.
TA: Jeongsu Kyeong
TA email: tuj64025@temple.edu
TA's Office Hour: 11:00 AM - 12:00 PM Tuesday, or by appointment.
Exams + Written Homework
Exams + Written Homework
Suggested Problems
Suggested Problems
Week 1: Ch 1, # 1 - 5
Week 2: Ch 1, # 6 - 14. Ch 2, # 1 - 11, 22, 23.
Week 3: Ch 2, # 12, 14, 15, 22 - 26.
Week 4: Ch 2, # 13, 16, 17, 18, 19, 24 - 30.
Week 5: Ch 3, # 1 - 5, 20, 21, 22, 23, 24*, 25*.
Week 6: ^^
Week 7: Ch 3 # 6, 7, 8, 11, 12, 14, 16, 17, 19 - 25.
Week 8: Ch 4 # 1 - 7
Week 9: Ch 4 # 8 - 16
Week 10: Ch 4 # 19 - 24.
Week 11: Ch 5 # 1 - 8.
Week 12: Ch 5 # 9, 10, 11, 16, 19*, 21, 25*
Week 13: Ch 7 # 1 - 9.
Lecture Notes and Reading Schedule
Lecture Notes and Reading Schedule
Lecture 1 - Introduction.
Reading: Ch 1 up to Prop 1.18. Try and understand the proofs and write down where you are confused.
Lecture 2 - Least Upper Bounds, Fields and the Real Numbers.
Reading: Ch 1, rest of the chapter.
Lecture 3 - Archimedean Proprerty, Density, n-th Roots, The Complex Field.
Reading: Rest of Ch 1, and Ch 2 up to Thm 2.14.
Lecture 4 - Countability.
Reading: Up to Thm 2.30.
Lecture 5 - Metric Space Topology.
Reading: Re-read everything from the last 3 readings.
Lecture 6 - More Metric Space Topology.
Reading: Up to Theorem 2.42 (Compactness)
Lecture 7 - Compactness
Reading: Continue reading thru Theorem 2.42.
Lecture 8 - Compactness, Part II
Reading: Finish Ch 2.
Lecture 9 - Compactness, Part III
Reading: Finish Ch 2.
Lecture 10 - Compactness, Part IV
Reading: Ch 3 up to Theorem 3.7.
Lecture 11 - Cantor Set.
Reading: Ch 3 up to Defn 3.8.
Lecture 12 - Sequences
Reading: Ch 3 up to Thm 3.14.
Lecture 13 - Convergence
Reading: Ch 3 up to Thm 3.14.
Lecture 14 - Subsequences
Reading: Ch 3 up to Thm 3.17.
Lecture 15 - Cauchy Sequences, Part I
Reading: Ch 3 up to Thm 3.20
Lecture 16 - Cauchy Sequences, Part II
Reading: Ch 3 up to Thm 3.22
Lecture 17 - Liminf and Limsup
Reading: Study for the exam!
Lecture 18 - Exam 1 Review
Reading: Exam Review
Lecture 19 - Examples of real sequences, Thm 3.20 and Intro to Series
Reading: Up to Thm 3.28.
Lecture 20 - Comparison Test and Geometric Series
Reading: Up to Thm 3.28.
Lecture 21 - p Series test
Reading: Up to Thm 3.34
Lecture 22 - e and the Root Test
Reading: Up to Example 3.40.
Lecture 23 - Ratio Test and Proof Discussion
Reading: ...
Lecture 24 - More Proof Discussion and Power Series
Reading: Ch 4 up to Thm 4.8
Lecture 25 - Limits and Continuity, Intro
Reading: ...
Lecture 26 - Limits and Continuity, Part II
Reading: Up to Thm 4.19.
Lecture 27 - Compactness and Continuity
Reading: Up to Example 4.27
Lecture 28 - Uniform Continuity
Reading: Finish Chapter 4
Lecture 29 - Discontinuities and Monotonicity
Reading: Study for Exam 2
Lecture 30 - Exam 2 Review
Study for the Exam!
Exam 2
Reading: Ch 5 up to the Mean Value Theorem.
Lecture 31 - Derivatives
Reading: Up to Thm 5.12
Lecture 32 - Mean Value Theorem
Reading: End of Ch 5.
Lecture 33 - L'Hopital's Rule
Reading: Taylor's Theorem
Lecture 34 - Taylor's Theorem
Reading: Ch 7 up to Thm 7.15.
Lecture 35 - Uniform Convergence of Sequences of Functions
Reading: Ch 7 up to Thm 7.15.
Lecture 36 - Uniform Convergence and Continuity
Reading: Ch 7 up to Thm 7.18
Lecture 37 - The space C(X) and Uniform Convergence + Differentiability
Reading: Understand the statements of Thm 7.25 and 7.26 and the definition of equicontinuity.
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