Analysis and Probability I


  • Instructor: Prof. Ioannis Karatzas
    • 11:00-12:15pm on TuTh, 312 Math
    • Office hour: Announced in the first class
  • Syllabus
  • Projected Final Exam Schedule: Tuesday Dec 18 9:00-noon.
  • Reccomended Textbooks for exercises
    • P. Billingsley: Probability and Measure
    • C.D. Aliprantis & O. Burkinshaw: Problems in Real Analysis - A Workbook with Solutions.
  • TA: Tomoyuki Ichiba
    • email: ichiba -at- stat d0t columbia d0t edu
    • Office hour: Tu 6:00-7:00 PM(Statistics Lounge on the 9th Floor)
    • Recitation:
      • Tu 7:10-8:00 PM(412 Pupin)( The room and time were changed .)
      • Th 8:00-9:00 PM (520 Math)( The room was changed)

Downladable Course Materials

Notices and Announcements

  • Notes 1.1 was posted. (4 Sep.)
  • TA recitation started in the first week.(Exercise 1, 2, 4, 7, 8, 9 in section 1.1 )
  • Assignment 1 and 2 were posted(7 Sep.)
  • TA recitation in the second week(Exercise 1, 2, 4, 5, 6, 8 in section 1.2)
  • Notes 1.2 was posted. (11 Sep.)
  • Notes 1.2 was updated. (13 Sep.)
  • Notes 1.3 was posted. (13 Sep.)
  • Picture on Measure was posted. (15 Sep.)
  • First half of Notes 1.4, Appendix, and Assignment 3 was posted. (18 Sep.)
  • TA recitation in the third week(Exercise 1, 3, 4, 6, 8 in section 1.3)
  • Note 1.5 was posted. (20 Sep.)
  • TA recitation ;the rooms and time were changed.(21 Sep)
  • Assignment 4-5 were posted. (25 Sep.)
  • TA recitation in the fourth week(Exercise 5, 6 from section 1.4 and 5, 7, 13 in section 1.5)
  • Notes 1.6 was posted. (27 Sep.)
  • Notes 1.7 was posted. Also Appendix was corrected. (1 Oct.)
  • TA recitation in the fifth week(Exercise 1, 2, 3, 4 in section 1.6)
  • TA recitation in the sixth week(Exercise 1, 2, 3 in section 1.7 and other exercises from the previous sections)
  • New version of Notes 1.5, Notes 1.9 and a survey paper were posted. (12 Oct.)
  • Notes 2.1-2.2 and practice mid-terms were posted. (18 Oct.)
  • Notes 1.4 was updated. (18 Oct.)
  • TA recitation in the seventh week exercises from uniform integrability and ergodicity
  • Assignment 6-7 were posted. (22 Oct.)
  • TA recitation in the eighth week exercises 8, 9, 10, 11 in section 2.2
  • Notes 2.2, 2.3, 2.5 and 1.10 were posted. (31 Oct.)
  • TA recitation in the nineth week exercises 1, 2, 3, 4, 5 in section 2.3
  • TA recitation in the tenth week exercises 1, 2, 3, 6 in section 2.5
  • Notes 2.4 and 2.6 were posted. (8 Nov.)
  • Mid term examination: mean = 19.26, standard deviation = 6.81
  • TA recitation in the eleventh week exercises 2.3.7, 2.3.8, 2.4.10 and 2.6.1
  • Assignment 8-9 were posted. (15 Nov.)
  • Notes 1.6 and 2.4 were updated. (15 Nov.)
  • Recommended textbooks are added.
  • Notes 3.1 was posted. (15 Nov.)
  • Notes 3.2-3.3 were posted. Notes 1.4, 1.7 were updated(20 Nov.)
  • Notes 3.4 was posted. (27 Nov.)
  • TA recitation in the twelveth week exercises from sections 3.1-3.3
  • Notes 2.9 was posted. (29 Nov.)
  • Assignment 10 was posted. (3 Dec.)
  • TA recitation in the thirteenth week exercises from sections 3.1-3.3 and 2.9
  • New Notes 3.4 was posted. (4 Dec.)
  • On coming Tuesday(11 Dec.) we have a class.
  • Paper by M.A. Pinsky was posted. (11 Dec.)
  • TA recitation in the fourteenth (last) week exercises from sections 2.9 and other problems as review of the whole semester.(Same days Same places)
  • Notes 2.9 was updated. (11 Dec.)
  • Sample final exam was posted in assignment section. (11 Dec.)