Felipe A. Ramírez
current semester
Metric Number Theory
| week | lecture 1 | lecture 2 |
|---|---|---|
| 1. Metric phenomena | Overview: normality, equidistribution, Dirichlet | Overview: Khintchine, Duffin–Schaeffer, Jarnik–Besicovitch; Equivalents to Borel's theorem |
| 2. Normality | Borel–Cantelli, Chebyshev's inequality, Proof of Borel | Probabilistic viewpoint, ergodic theoretic viewpoint |
| 3. Equidistribution | A bit more ergodic theory; equidistribution | Weyl's criterion, Van Der Corput, polynomial sequences |
| 4. Metric equidistribution | Metric questions for \((n\alpha)\); \(L^2\) arguments | Davenport–Erdős–LeVeque; pivot to Diophantine approximation |
Elementary Statistics
Homework: I will post assigned reading and exercises here every week. Section numbers and exercise numbers refer to Mind on Statistics, by Utts and Heckard, 5th edition.
Submission: Deliver a neatly-stapled hard copy to the portfolio labeled "MATH 132 HW" outside my office, 619 Exley.
| due | read | exercises (solutions) |
|---|---|---|
| Sept 18 | 2.1–2.7 | 2.3, 2.5, 2.11, 2.21, 2.22, 2.25, 2.30, 2.35, 2.59, 2.74 |
| Sept 25 | 3.1–3.5 | 2.37, 2.66, 2.94, 2.96, 3.2, 3.18, 3.22, 3.28, 3.34, 3.38, 3.44 |
| Oct 2 | 4.1, 4.3, 5.1, 5.3–5.6 | 3.47, 3.72, 3.81, 3.82, 4.4, 4.28, 5.3, 5.13, 5.16 |
| Oct 9 | 6.1, 7.1–7.4 | 6.4, 6.5, 6.14, 7.3, 7.7, 7.20, 7.22, 7.26, 7.30, 7.38 |
| Oct 16 | ||
| Oct 23 | ||
| Oct 30 | ||
| Nov 6 | ||
| Nov 13 | ||
| Nov 20 | ||
| Nov 27 | Thanksgiving | |
| Dec 3 | ||
| Dec 10 |
Classroom height data: 71, 61, 64, 68, 67, 67, 68, 68, 63, 65, 64, 68, 71, 66, 71, 64, 70, 65, 68, 61, 67, 68, 62, 65, 74, 67, 73, 63, 74, 69, 68, 72, 74, 61, 70, 64, 63, 60, 69, 72, 67
past semesters
| year | fall | spring |
|---|---|---|
| 2026/27 | Elementary Statistics; Metric Number Theory (graduate topics) |
Introduction to Real Analysis; Stochastic Processes |
| 2025/26 | Probability Theory; Differential Equations |
Measure Theory and Functional Analysis (graduate); Advanced Topics in Real Analysis |
| 2024/25 | Complex and Real Analysis (graduate); Fundamentals of Analysis |
Sabbatical |
| 2023/24 | Fundamentals of Analysis; Elementary Statistics |
Advanced Topics in Real Analysis; Fractal Geometry (graduate) |
| 2022/23 | Sabbatical | Measure Theory and Functional Analysis (graduate); Differential Equations |
| 2021/22 | Probability Theory; Discrete Mathematics |
Metric Number Theory (graduate topics); Calculus II |
| 2020/21 | Complex Analysis; Fractal Geometry (graduate) |
Multivariable Calculus; Calculus II |
| 2019/20 | Advanced Topics in Real Analysis; Complex and Real Analysis (graduate) |
Fundamentals of Analysis; Calculus II |
| 2018/19 | Sabbatical | Functional Analysis (graduate); Differential Equations |
| 2017/18 | Probability Theory | Measure Theory (graduate); Fundamentals of Analysis |
| 2016/17 | Multivariable Calculus; Complex Analysis (graduate) |
Differential Equations; Vectors and Matrices |
| 2015/16 | Probability Theory; Dynamics and Diophantine Approximation (graduate topics) |
Fundamentals of Analysis; Vectors and Matrices |