College of the Holy Cross, Fall 2021
Syllabus for Math 361 (Real Analysis I)
Professor Hwang, (rhymes with song)
Do not make travel plans that conflict with the midterm tests or your final exam. If an emergency prevents you from taking the final exam at the allotted time, speak to your Class Dean immediately to arrange for an incomplete grade, and to me to schedule a make-up exam.
The schedule below is subject to minor changes. Any substantial corrections will be announced by email and/or in class.
| Day | Date | Section | Topics |
| M | Aug 30 | Advising | |
| W | Sep 1 | Section 1 | Real Numbers |
| F | Sep 3 | Section 2.1-2.2 | Intervals and Bounds |
| M | Sep 6 | Section 2.3 | The Archimedean Property |
| W | Sep 8 | Section 2.4 | Topology |
| F | Sep 10 | Section 3.1 | Convergence |
| M | Sep 13 | Section 3.2-3.3 | Properties of Limits |
| W | Sep 15 | Section 3.5 | Subsequences, Cauchy Sequences |
| F | Sep 17 | Section 3.6 | Infinite Series |
| M | Sep 20 | Section 3.7 | Absolute Summability |
| W | Sep 22 | Section 4.1-4.2 | Functions, Composition, Inversion |
| F | Sep 24 | Midterm 1 | |
| M | Sep 27 | Section 4.3 | Cardinality |
| W | Sep 29 | Section 4.4 | Power Series |
| F | Oct 1 | Section 5.1 | Continuity |
| M | Oct 4 | Section 5.2 | Limits |
| W | Oct 6 | Section 5.3 | Landau Notation, Power Series |
| F | Oct 8 | Section 5.4 | The Intermediate Value Theorem |
| M | Oct 11 | Fall Break | |
| W | Oct 13 | Fall Break | |
| F | Oct 15 | Fall Break | |
| M | Oct 18 | Section 5.5 | The Extreme Value Theorem |
| W | Oct 20 | Section 6.1-6.2 | Properties of the Integral |
| F | Oct 22 | Midterm 2 | |
| M | Oct 25 | Section 6.3 | Integrability |
| W | Oct 27 | Section 6.4 | Definite Integrals |
| F | Oct 29 | Section 7.1-7.2 | Differentiability |
| M | Nov 1 | Section 7.3 | The Mean Value Theorem |
| W | Nov 3 | Section 8.1 | The Fundamental Theorems |
| F | Nov 5 | Section 8.2 | Taylor's Theorem |
| M | Nov 8 | Section 9.1 | Exp |
| W | Nov 10 | Section 9.2 | Representations of Exp |
| F | Nov 12 | Section 10.1 | Sine and Cosine |
| M | Nov 15 | Section 10.2 | Periodicity |
| W | Nov 17 | Section 11.1 | Normed Vector Spaces |
| F | Nov 19 | Section 11.2 | Metric Spaces |
| M | Nov 22 | Midterm 3 | |
| W | Nov 24 | Thanksgiving | |
| F | Nov 26 | Thanksgiving | |
| M | Nov 29 | Section 11.3 | Open and Closed Sets |
| W | Dec 1 | Section 11.5-11.6 | Boundedness and Compactness |
| F | Dec 3 | Section 11.6 | Compactness |
| M | Dec 6 | Section 12.1 | Sequences in Metric Spaces |
| W | Dec 8 | Section 12.2 | Continuity of Mappings |
| F | Dec 10 | Section 12.4 | Uniform Limits |