Further Topics in Probability, Autumn 2013
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Tel: | +44 (0)117 928-7991 | |
| Office: | Maths 3.7 | |
| Office hours: | Mondays 10:00 - 10:45am in teaching weeks, Maths 3.7 | |
| except for the 28th of October, which is cancelled. |
|
Below is a detailed schedule. Topics of future events are plans, and can change. Topics of past events serve as log.
Homeworks are/will also be posted here: just click those with a link below. They are due in class, or in the blue locker with my name on the ground floor of the Main Maths Building.
If everything works as intended (second try on 21 Oct, 12:15), homework solutions can be found in Blackboard under MATH30006_2013 or MATHM0018_2013. Please email me if you have problem accessing these.
| Day | Topics | Homework due: |
|---|---|---|
| Mon 30 Sep, 11:00, Maths PC3 | Review of the unit, basic discrete distributions | -- |
| Tue 1 Oct, 2:00, Phys 3.34 | Convolution (discrete cases) | -- |
| Wed 2 Oct, 10:00, Phys 3.27 | Convolution (Gaussian) | -- |
| Thu 3 Oct, 9:00, Maths PC4 | Tutorial: Neg.Binom and Uniform convolution; Residue Thm. | -- |
| Mon 7 Oct, 11:00, Maths PC3 | Convolution (Cauchy) | -- |
| Tue 8 Oct, 2:00, Phys 3.34 | Convolution (Cauchy, Exponential) | -- |
| Wed 9 Oct, 10:00, Phys 3.27 | Poisson process, Chi square; Generating functions (properties) | HW1 |
| Thu 10 Oct, 9:00, Maths PC4 | Tutorial (Convolutions, generating functions) | -- |
| Mon 14 Oct, 11:00, Maths PC3 | Generating functions (examples; of convolutions) | -- |
| Tue 15 Oct, 2:00, Phys 3.34 | Generating functions (random no. of summands, Galton-Watson process) | -- |
| Wed 16 Oct, 10:00, Phys 3.27 | Generating functions (Galton-Watson process) | -- |
| Thu 17 Oct, 9:00, Maths PC4 | Tutorial (Generating functions) | -- |
| Mon 21 Oct, 11:00, Maths PC3 | Generating functions (random walk: level 1 hitting time) | -- |
| Tue 22 Oct, 2:00, Phys 3.34 | Generating functions (random walk) | -- |
| Tue 22 Oct, 3:00, SM2 | Generating functions (Poisson approximation) | -- |
| Wed 23 Oct, 10:00, Phys 3.27 | Renewal Theory (LLN) | HW2 |
| Thu 24 Oct, 9:00, Maths PC4 | Tutorial (Generating functions) | -- |
| Fri 25 Oct, 11:00, Maths SM3 | Renewal Theory (LLN, Delayed renewals) | -- |
| I am away the whole week | ||
| Mon 4 Nov, 11:00, Maths PC3 | Renewal Theory (Stationary renewals, Blackwell's Thm) | -- |
| Tue 5 Nov, 2:00, Phys 3.34 | Renewal Theory (Renewal equation) | -- |
| Tue 5 Nov, 3:00, SM2 | Tutorial (Generating fcts, Moran's example) | -- |
| Wed 6 Nov, 10:00, Phys 3.27 | Renewal Theory (Renewal Thm, examples) | HW3 |
| Thu 7 Nov, 9:00, Maths PC4 | Tutorial (Age, renewal paradox, length biased sampling) | -- |
| Fri 8 Nov, 11:00, Maths PC4 | Weak Law of Large Numbers, Stirling's formula | -- |
| Mon 11 Nov, 11:00, Maths PC3 | Stirling's formula, DeMoivre Laplace CLT | -- |
| Tue 12 Nov, 2:00, Phys 3.34 | DeMoivre Laplace CLT | -- |
| Wed 13 Nov, 10:00, Phys 3.27 | Measure Theory (basic notions, probability) | -- |
| Thu 14 Nov, 9:00, Maths PC4 | Tutorial (Renewal Thm) | -- |
| Mon 18 Nov, 11:00, Maths PC3 | Measure Theory | -- |
| Tue 19 Nov, 2:00, Phys 3.34 | Probabilistic tools | -- |
| Wed 20 Nov, 10:00, Phys 3.27 | Probabilistic tools, notions of convergence | HW4 |
| Thu 21 Nov, 9:00, Maths PC4 | Tutorial (DeMoivre Laplace Thm, types of convergences) | -- |
| Mon 25 Nov, 11:00, Maths PC3 | Strong Law of Large Numbers (Kolmogorov's inequality) | -- |
| Tue 26 Nov, 2:00, Phys 3.34 | Strong Law of Large Numbers (Kolmogorov-Khinchin, Toeplitz, Kronecker) | -- |
| Wed 27 Nov, 10:00, Phys 3.27 | Strong Law of Large Numbers (Kolmogorov's Thm, SLLN) | -- |
| Fri 29 Nov, 9:00, Maths PC4 | Tutorial (Types of convergences, LLN) | -- |
| Mon 2 Dec, 11:00, Maths PC3 | SLLN, Characteristic Functions | -- |
| Tue 3 Dec, 2:00, Phys 3.34 | Characteristic Functions | -- |
| Wed 4 Dec, 10:00, Phys 3.27 | Characteristic Functions (Inversion formula) | HW5 |
| Thu 5 Dec, 9:00, Maths PC4 | Tutorial (LLN, Characteristic functions) | -- |
| Mon 9 Dec, 11:00, Maths PC3 | Weak Convergence (relative compactness, tightness) | -- |
| Tue 10 Dec, 2:00, Phys 3.34 | Weak Convergence, CLT (Prokhorov's Thm) | -- |
| Wed 11 Dec, 10:00, Phys 3.27 | Weak Convergence, CLT (Continuity Lemma) | -- |
| Thu 12 Dec, 9:00, Maths PC4 | Tutorial (Characteristic functions) | -- |
| Mon 16 Dec, 11:00, Maths PC3 | Weak Convergence, WLLN, CLT | -- |
| Tue 17 Dec, 2:00, Phys 3.34 | Weak Convergence, CLT (Comments to the CLT) | -- |
| Wed 18 Dec, 10:00, Phys 3.27 | Weak Convergence, CLT (Coupon collector, elements of Large Deviations) | HW6 |
| Thu 19 Dec, 9:00, Maths PC4 | Tutorial (LLN, Characteristic functions, Lindeberg Thm) | -- |
If you have any questions, please contact me (see on top). Below is my schedule.
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