MATH30006, MATHM0018
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Office: | 1.44 Fry (but I think you are not allowed up here...) | |
| Math cafés: | Tuesdays 5:00pm, Zoom (see link on Blackboard) | |
| Drop in Sessions: | Tuesdays 14:30 - 15:30, Zoom (see link on Blackboard) | |
| Q&A Session: | Thursday 3rd June, 2:00pm, Zoom. Please prepare with questions. |
|
Below is a detailed schedule. Topics of future events are plans, and can change. Topics of past events serve as log. The green version of pdf's use less paper to print. Blended teaching will manifest in prerecorded videos and live teaching on Zoom.
Videos can be found under the links below, and I will also back them up on Blackboard. (At some point the numbering changes from Ln to Fn. This has no significance, it's just where we switch to last year's videos; at that time I had no idea that I'll still be recording this unit a year later.) The Zoom meeting links will be announced at least a few days in advance on Blackboard and by email. The recommended literature can be found under the unit description links above. These are advisory, examinable is what is featured in lectures.
Homeworks are/will also be posted here: just click those with a link below. They are due every second Thursday (see below) at 12:00pm in Blackboard. Homework solutions will appear on Blackboard, please email me if you have problem accessing these.
| Time | Where | Topics | Watch prerecorded: | Homework due: |
|---|---|---|---|---|
| by Mon 1 Feb | At home | Intorduction and overview of the unit | L0 | -- |
| by Thu 4 Feb | At home |
Basic discrete distributions Convolution (discrete cases) Basic continuous distributions |
L1,
L2 L3, L4, L5, L6 L7 |
-- |
| Fri 5 Feb, 10:00am | Zoom | Live ex. class (continuous convolution) | -- | |
| by Thu 11 Feb | At home |
Normal distribution Convolution (Uniform, Gaussian) Convolution (Cauchy) |
L8 L9, L10 L11, L12, L13 |
by Thu 11 Feb, noon:
HW1 (sol. on Bb.) |
| Fri 12 Feb, 10:00am | Zoom | Live ex. class (Convolution comments and examples) | -- | |
| by Thu 18 Feb | At home |
Gamma, Chi square distributions Poisson process Generating functions (properties) |
L14,
L15,
L16 L17 L18, L19, L20, L21, L22, L23 |
-- |
| Fri 19 Feb, 10:00am | Zoom | Live ex. class (generating function examples) | -- | |
| by Thu 25 Feb | At home |
Generating functions (random no. of summands) Generating functions (Galton-Watson process) |
L24,
L25 L26, L27, L28, L29, L30 |
by Thu 25 Feb, noon:
HW2 (sol. on Bb.) |
| Fri 26 Feb, 10:00am | Zoom | Live ex. class (Critical G-W process; random walk) | -- | |
| by Thu 4 Mar | At home |
Generating functions (random walk: level 1 hitting time) Generating functions (weak convergence) |
L31,
L32,
L33 L34, L35, L36 |
-- |
| Fri 5 Mar, 10:00am | Zoom | Live ex. class (fun with generating functions) | -- | |
| by Thu 11 Mar | At home |
Weak convergence Weak Law of Large Numbers Stirling's formula |
L37 L38, L39 L40, L41 |
by Thu 11 Mar, noon:
HW3 (sol. on Bb.) |
| Fri 12 Mar, 10:00am | Zoom | Live ex. class (Generating functions: RW probabilities (sol. on Bb)) | (E1 on Bb.) | -- |
| by Thu 18 Mar | At home |
DeMoivre Laplace CLT Measure Theory (basic notions, probability) (videos borrowed from Martingales) |
L42,
L43,
L44,
L45,
L46 M1, M2 |
-- |
| Fri 19 Mar, 10:00am | Zoom | Live ex. class (DeMoivre Laplace CLT) | -- | |
| by Thu 25 Mar | At home |
Measure Theory (videos borrowed from Martingales) A product-sum lemma, probabilistic tools |
L47,
M3,
M4,
M5,
M6 F1, F2, F3, F4 |
by Thu 25 Mar, noon:
HW4 (sol. on Bb.) |
| Thu 26 Mar 10:00am | Zoom | Live ex. class (probabilistic tools) | -- | |
| Easter vacation | ||||
| by Thu 22 Apr | At home |
Probabilistic tools and inequalities Modes of convergence SLLN (Kolmogorov's ineq.) |
F5,
F6,
F7,
F8,
F9 F10, F11, F12 F13, F14 |
-- |
| Fri 23 Apr, 10:00am | Zoom | Live ex. class (convergence modes) | (E2, E3, E4, E5) | -- |
| by Thu 29 Apr | At home |
SLLN (Kolmogorov-Khinchin; Toeplitz' lemma; Kronecker) SLLN (Kolmogorov's Thm, final proof, remarks) Characteristic Functions |
F15,
F16,
F17 F18, F19, F20, F21, F22 F23, F24, F25, F26, F27 |
by Thu 29 Apr, noon:
HW5 (sol. on Bb.) |
| Fri 30 Apr, 10:00am | Zoom | Live ex. class (Characteristic functions (sol. on Bb)) | (E6, E8 on Bb.) | -- |
| by Thu 6 May | At home |
Inversion formula Weak convergence Weak Convergence (Prokhorov's Thm) |
F28,
F29 F30 F31, F32 |
-- |
| Fri 7 May, 10:00am | Zoom | Live ex. class (Characteristic functions (sol. on Bb)) | (E7, E9 on Bb.) | -- |
| by Thu 13 May | At home |
Continuity Lemma WLLN, CLT |
F33,
F34,
F35,
F36 F37, F38, F39 |
by Thu 13 May, noon:
HW6 (sol. on Bb.) |
| Fri 14 May, 10:00am | Zoom | Live ex. class (Comments on the CLT ) | (E10, E11 on Bb.; F40, F41, F42) | -- |
If you have any questions, please contact me (see on top). Click here to see my schedule.
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