Further Topics in Probability, Autumn 2013
Márton Balázs  
Email:  m.balazs@our_city.ac.countrycode  
Tel:  +44 (0)117 9287991  
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, GaltonWatson process)   
Wed 16 Oct, 10:00, Phys 3.27  Generating functions (GaltonWatson 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 (KolmogorovKhinchin, 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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