Math 112
Introduction to Analysis, Spring 2024 (Section S01)Current week | Moodle | Course information
Instructor: David Perkinson (schedule)
Course lecture notes: Math 112 Lecture Notes, by David Perkinson. (To be revised throughout the semester. Last update: 8/23/24.)
Exercises: compiled homework problems and compiled group problems.
Supplemental text: Introduction to Analysis, by Irena Swanson.
LaTeX Overleaf pointers
For details on office hours and drop-in tutoring, see the top of our Moodle page.
Final exam: We will have an in-class final exam, May 8, 1–4 pm, L204. Review sheet.
NOTE: The location of our final exam has changed from E314 to L204.
Week 1: January 25 - 29
Monday: Welcome. Preliminaries, LaTeX.
To do list for Wednesday.
Wednesday: Induction.
Reading for Wednesday, Week 1. Supplemental reading: sections 1.4 and 1.5 in Swanson.
Lecture/quiz. (Do the reading before watching this video lecture.).
Group problems. Solutions.
Friday: Sets.
Reading for Friday, Week 1. Supplemental reading: Section 2.1 in Swanson.
Lecture/quiz.
Turn in: HW1F (overleaf template).
Group problems. Solutions.
Week 2: January 29 - February 2
Monday: More sets. Cartesian products.
Reading for Monday, Week 2. Also read Mathematical Writing. Supplemental reading: Sections 2.1 and 2.2 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Wednesday: Relations and equivalence relations.
Reading for Wednesday, Week 2. Supplemental reading: Section 2.3 in Swanson.
Lecture/quiz. (The lecture makes reference to the notation \([n]:=\{1,\dots,n\}\), which conflicts with our use of square brackets to denote equivalence classes. Context should make the meaning clear.)
Group problems: Solutions.
Friday: Equivalence classes, \(\mathbb{Z}/n\mathbb{Z}\).
Reading for Friday, Week 2. Supplemental reading: Section 2.3 in Swanson.
Lecture/quiz.
Turn in: HW2F, (overleaf template).
Week 3: February 5 - 9
Monday: Functions.
Reading for Monday, Week 3. Supplemental reading: Section 2.4 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Wednesday: More functions.
Reading for Wednesday, Week 3. Note: This reading is a bit longer then the others. Supplemental reading: Section 2.4 in Swanson.
Lecture/quiz.
Group problems: Solutions.
Friday: Modular arithmetic.
Reading for Friday, Week 3. Supplemental reading: Example 2.3.10 in Swanson.
Lecture/quiz.
Turn in: HW3F, (overleaf template). Here are a few pointers for typesetting functions: typesetting functions.
Group problems: Solutions.
Week 4: February 12 - 16
Monday: Something awesome (cardinality).
Exam distributed today (review sheet). No reading or lecture/quiz for today.
Group problems. Solutions.
Wednesday: More awesome (more cardinality).
Exam due by noon today.
No reading or lecture/quiz for today.
Group problems: Solutions.
Friday: Field axioms.
Reading for Friday, Week 4. Supplemental reading: Section 2.6 in Swanson.
Lecture/quiz.
Turn in: HW4F, (overleaf template).
Group problems: Solutions.
Week 5: February 19 - 23
Monday: Order axioms.
Reading for Monday, Week 5. Also read Addendum to Friday, Week 4 (more examples of consequences of the field axioms). Supplemental reading: Sections 2.6 and 2.7 in Swanson.
Lecture/quiz,
Group problems. Solutions.
Wednesday: Completeness.
Reading for Wednesday, Week 5.
Lecture/quiz,
Exam 1 resubmissions due today via Gradescope.
Group problems: Solutions.
Friday: Extrema.
Reading for Friday, Week 5. Supplemental reading: Section 2.7 in Swanson.
Lecture/quiz.
Turn in: HW5, (overleaf template).
Group problems. Solutions.
Week 6: February 26 - March 1
Monday: Complex numbers I.
Reading for Monday, Week 6. Supplemental reading: Section 3.1 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Wednesday: Complex numbers II.
Reading for Wednesday, Week 6. Supplemental reading: Sections 3.2 and 3.3 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Friday: Complex numbers III.
Reading for Wednesday, Week 6. Supplemental reading: Section 3.4 in Swanson.
Lecture/quiz.
Turn in: HW6, (overleaf template).
Group problems. Solutions.
Week 7: March 4 - 8
Monday: Topology.
Reading for Monday, Week 7. Supplemental reading: Section 3.5 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Wednesday: Sequences I.
Reading for Wednesday, Week 7. Supplemental reading: Start reading chapter 8 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Friday: Sequences II.
Reading for Friday, Week 7. Supplemental reading: Start reading chapter 8 in Swanson.
Lecture/quiz.
Turn in: HW7, (overleaf template).
Group problems. Solutions.
Week 8: March 18 - 22
Monday: In class (easy) exam (review sheet) .
No reading or lecture/quiz for today.
Wednesday: Something awesome.
Exam~2 distributed by noon today (review sheet). [Change: the Exam 2 was distributed at the beginning of Spring Break.]
No reading or lecture/quiz for today.
Group problems. Solutions.
Friday: More awesome.
Exam 2 due by noon today.
No reading or lecture/quiz for today.
Related videos: The Mandelbrot Set and Filled Julia Set. For experimentation: Julia set web app.
Group problems. Solutions.
Week 9: March 25 - 29
Monday: New-from-old limit theorem.
Reading for Monday, Week 9. Supplemental reading: Theorem 8.4.3 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Wednesday: Monotone Convergence Theorem.
Reading for Wednesday, Week 9. Supplemental reading: Section 8.6 in Swanson.
Lecture/quiz.
Group problems. Solutions.
Friday: Sequences III.
Reading for Friday, Week 9. Supplemental reading: Sections 8.3, 8.4, 8.7, and 8.8 in Swanson. Recommended reading: Discrete dynamical systems.
Lecture/quiz.
Turn in: HW9 (overleaf template).
Week 10: April 1 - 5
Monday: Series. Geometric series.
Reading for Monday, Week 10. Supplemental reading: Section 9.1 in Swanson.
Lecture/quiz.
Note: There will be a short quiz at the beginning of class this Friday. It will just ask you for the definition of the limit of a sequence as it appears on page 1 of the lecture for Wednesday, Week 7.
Group problems. Solutions.
Wednesday: Series tests I.
Reading for Wednesday, Week 10. Supplemental reading: Section 9.2 in Swanson.
Lecture/quiz.
Exam 2 resubmissions due today via Gradescope.
Friday: Series tests II.
Reading for Friday, Week 10. Supplemental reading: Section 9.2 in Swanson.
Lecture/quiz.
Quiz today. Class will begin with a short quiz asking you for the definition of the limit of a sequence as it appears on page 1 of the lecture for Wednesday, Week 7.
Turn in: HW10 (overleaf template).
Group problems. Solutions.
Week 11: April 8 - 12
Monday: Series tests III.
Reading for Monday, Week 11. Supplemental reading: Section 9.2 in Swanson.
Lecture/quiz
Group problems. Solutions.
Wednesday: Limits of functions.
Reading for Wednesday, Week 11. Supplemental reading: Sections 4.1 and 4.2 in Swanson.
Lecture/quiz
Group problems. Solutions.
Friday: Continuity and derivatives.
Reading for Friday, Week 11. Supplemental reading: Sections 5.1, 6.1, and 6.2 in Swanson.
Lecture/quiz
Group problems. Solutions.
Turn in: HW11F (overleaf template).
Week 12: April 15 - 19
Monday: Power series I.
Reading for Monday, Week 12. Supplemental reading: Section 9.3 in Swanson.
Lecture/quiz
Group problems. Solutions.
Wednesday: Power series II.
Reading for Wednesday, Week 12. Supplemental reading: Sections 9.3 and 9.4 in Swanson.
Lecture/quiz
Note: There will be a short quiz at the beginning of class this Friday. It will just ask you for the definition of the limit of a sequence as it appears on page 1 of the lecture for Wednesday, Week 7 and for the definition of the limit of a function as it appears on page 2 of the lecture for Wednesday, Week 11.
Group problems. Solutions.
Friday: Taylor series I.
Reading for Friday, Week 12. Supplemental reading: Sections 6.5 and 9.7 in Swanson.
Lecture/quiz
Group problems. Solutions.
Turn in: HW12 (overleaf template).
Week 13: April 22 - 26
Monday: Taylor series II. The complex exponential function.
Reading for Monday, Week 13. Supplemental reading: Sections 6.5 and 9.7 in Swanson.
Lecture/quiz
Group problems. Solutions.
Wednesday: Two theorems from calculus.
Reading for Wednesday, Week 13. Supplemental reading: Sections 5.2 and 5.3 in Swanson.
Lecture/quiz
Group problems. Solutions.
Friday: Three theorems by Euler.
Reading for Friday, Week 13.
Lecture/quiz
Group problems. Solutions.
Turn in: HW13 (overleaf template).
Week 14: April 29 - May 3
Reading week.
Week 15: May 6 - 10
We will have an in-class final exam, May 8, 1–4 pm, E314.
Here is a
review sheet.
The \(\LaTeX\) document preparation system
- Most will find Overleaf the easiest way to get started. Here is the Overleaf 30 minute tutorial.
- \(\LaTeX\) (getting started in \(\LaTeX\))
- short guide
- Change .pdf to .tex in the URL of (nearly) any pdf file accessed from this page to get the \(\LaTeX\) source code.