120101 ESM3A Advanced Linear Algebra/Stochastic Processes

ESM3A is mandatory for students of EECS, and is also recommended as a home school elective for students who would like to learn more advanced topics from Probability (for most of the semester) and Linear Algebra (for about 4 weeks) than were covered in second semester Engineering and Science Mathematics. The course covers, after a repetition and deepening of basic probability concepts and univariate random variables as introduced in ESM2B, multivariate distributions, functions of one random variable (moments, characteristic function), limit theorems, and an introduction to basic discrete (Markov chains) and continuous-time stochastic processes (Poisson process, Brownian motion). In the linear algebra part, emphasis is on matrix factorizations (Jordan normal form, LU, QR, SVD) and their applications.

Instructor of Record:	Peter Oswald
Email:	p.oswald@jacobs-university.de,
Phone:	200-3179
Office hours:	Tuesdays 2-3:30pm (or by appointment) in Research I, 113

TA:	TBA
Email:
Tutorial:	Weekly (if demand warrants it)

Lectures :

Mo 9:45-11am and We 8:15-9:30am in the Lecture Hall of Research 3

• [GS] G.R. Grimmett, D.R. Stirzaker, Probability and Random Processes , 3rd edition, Oxford Univ. Press, 2001+ (good compromise between theory and examples).
• [D] S. Ghahramani, Fundamentals of Probability with Stochastic Processes , Pearson/Prentice Hall, 3rd edition, 2005 (less theoretical and less well-structured, tons of exercises and worked examples).
• [D] R. Durrett, Probability: Theory and Examples , Duxbury Press, 3rd edition, 2004 (more on the math side).
• [R] Gilbert Strang, Introduction to linear algebra, 3rd edition, Wellesley-Cambridge Press, 2003 (US style textbook covering many aspects of applied linear algebra, with many easy worked and self-study problems, relevant for this course are Chapters 6 and 7).
• [KK] Y. Katznelson, Y. R Katznelson, A (terse) Introduction to Linear Algebra , AMS, Providence RI, 2007 (secondary reading, if you are math-heavy).

Weekly homework will be announced in class and posted online. Check the website on a regular basis! Written solutions need to be turned in on the due date and in class (usually on the Wednesday of the following week), No late homework will be accepted. Note: Homework is your individual work, copying from others is against our Code of Academic Integrity, and will in the end backfire.

I will administer a certain number quizzes, they will be announced in class.

A Midterm Exam (probably during the week after the Fall reading days) and a Final Exam will be given. Exact dates and details about the exams will be given in class at a later time.

Calculators are not allowed at exams (major reason: fairness). A certain amount of calculating by hand is useful, and is supported by this policy.

Only valid and timely excuses (as regulated by Jacobs University policies, and confirmed by the registrar) will be accepted if you miss homework deadlines, or exams.

• The final grade will be computed from the weighted average of percentages of maximal scores with the weights

  Homework:	20%
  Quizzes:	10%
  Midterm Exam (approx. in Week 8):	30%
  Final Exam (examination period):	40%

  
  according to the following table:

  Cutoff score:	95%	90%	85%	80%	75%	70%	65%	60%	55%	50%	45%	40%
  IUB Points:	1.0	1.33	1.67	2.0	2.33	2.67	3.0	3.33	3.67	4.0	4.33	4.67