GRA6035 Mathematics - 2017/18

Reading

Reading for GRA 6035 Mathematics: Some additional/older material that could be useful for GRA 6035 Mathematics:

All material covered by the lectures and problems is part of the curriculum for GRA 6035 Mathematics, and is relevant for the final exam. All material covered by Lecture 1-6 and all problems corresponding to these lectures is relevant for the midterm exam. The list of sections in [ME] in the Lecture Plan below is indicative of the curriculum of  the course.

Lecture Plan

We offer lectures (3h/week, usually Fri 08-11 in A1-040, see lecture plan below), plenary session (4 x 3h, see lecture plan below), and exercise sessions (Mon/Tue afternoon, see plan below the lecture plan). In addition, you can see me in the office hours (weekly on Thu at 12.00 - 14.00 in my office B4-032). In plenary sessions, I will go through selected problems in the auditorium. In exercise sessions, you will work on problems on your own (or in groups), and teaching assistants will be present to help you. 

In the office hours, you can ask me for help with problems or ask other questions from the lectures. It is not necessary to make an appointment to see me in the office hours. It is often possible to see me outside office hours (come by to see if I am available, or make an appointment). I will be in my office most of the time Mon-Fri, except Thu 08-11 when I teach another course.

The lecture plan is tentative, and may be changed/updated during the semester. In some cases, only parts of the sections indicated in the Reading column is required for this course (material in parantheses is not core material, but still useful to read to link the mathematics in the course to applications). Lecture notes will be uploaded as they become available (typically soon after the lecture).

Date: Topic:  Reading: Problems:
Aug 2017 FORK 1003: Mathematics module (preparatory course)    
Fri Aug 25
0800-1045 : A1-040
Lecture 1
Linear systems and Gaussian Elimination. Rank.
[ME] 6.1, (6.2), 7.1 - 7.4, (7.5)
[LSGE] 1 - 3
Workbook
Lecture 1 
Fri Sep 01
0800-1045 : A1-040  
Lecture 2
Matrices and Matrix Algebra
[ME] 8.1 - 8.4, (8.5 - 8.6), 9.1 - 9.2, (9.3),
26.1 - 26.3, (26.4), 26.5
Workbook
Lecture 2
Tue Sep 05
1800-1945 : C2-020/030
First Excercise Session
Problems from Lecture 1-2
Fri Sep 08
0800-1045 : A1-040
Lecture 3
Vectors and Linear Independence
[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1
 
Workbook
Lecture 3
Fri Sep 15
0800-1045 : A1-040
Lecture 4
Eigenvalues and Diagonalization
[ME] 23.1 - 23.4, 23.6 -23.7, (23.9)
 
Workbook
Lecture 4
Mon Sep 18
1700-1945 : A1-040
Plenary Session 1
Problems from Lecture 1-4 + [ODE] Integration
Workbook 1.15, 2.18b, 3.12, 3.14, 4.5, 4.9, 4.10, 4.11, 4.12
Midterm Exams
10/2016 Pb 1, 10/2014 Pb 3, 03/2016 Pb 3, 10/2015 Pb 4
Fri Sep 22
0800-1045 : A1-040
Lecture 5 - Notes: How to compute all principal minors
Markov chains. Quadratic Forms and Definiteness
[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8  
Application of eigenvectors: Google's PageRank algorithm
Workbook
Lecture 5
Fri Sep 29
1700-1945 : A1-040
Lecture 6  - New result on semidefiniteness
Unconstrained Optimization
[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1
 
Workbook
Lecture 6
Fri Oct 06
0800-1045 : A1-040
Lecture 7
Constrained Optimization and First Order Conditions
[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1
 
Workbook
Lecture 7
Mon Oct 09
1700-1945 : A1-040
Plenary Session 2
Problems from Lecture 4-6 + Midterm Exam 10/2016
Workbook: 4.3b, 4.10, 5.9, 5.15, 6.1c, 6.12
Midterm 10/2016 Problem 1-8, Midterm 03/2016 Problem 5,7,8
Fri Oct 13
0800-1045 : A1-040
Lecture 8 - Notes: Proof of SOC, Alternative method for NDCQ
Constrained Optimization and Second Order Conditions
[ME] 19.1, (19.4)
 
Workbook
Lecture 8 
Fri Oct 13
1500-1600
Midterm exam 13/10/2017 - Solution
Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
Fri Oct 20
0800-1045 : A1-040
Lecture 9
Envelope Theorems and Bordered Hessians
[ME] 19.2 - 19.3, (19.4 - 19.6)
 
Workbook
Lecture 9
Fri Oct 27
0800-1045 : A1-040
Lecture 10
First order differential equations
[ME] 24.1 - 24.2, (24.4 - 24.6)
[ODE] Differential Equations 1.1 - 1.7
Workbook
Lecture 10
Mon Oct 30
1700-1945 : A1-040
Plenary Session 3
Problems from Lecture 7-9
Workbook 7.1, 7.8/8.7, 7.11/8.10, 8.13, 8.8, 8.12
Exam 12/2015 Problem 3-4 Exam 01/2017 Problem 3-4
Fri Nov 10
0800-1045 : A1-040
Lecture 11
Stability. Second order differential equations. Systems of differential equations.
[ME] 24.1 - 24.3, (24.4 - 24.6)
[ODE] Differential Equations 1.8 - 1-10, 2.1 - 2.2
Workbook
Lecture 11
Mon Nov 13
1700-1945 :A1-040
Plenary Session 4
Problems from Lecture 10-11
Workbook 10.8, 10.12, 10.15, 11.6, 11.11 [ODE] Differential
Equations 1.14, 1.24, 2.3 Exam 01/2017 Problem 2
Fri Nov 17
0800-1045 : A1-040
Lecture 12
Systems of differential equations. Difference Equations.
[ME] 23.2
[ODE] Differential Equations 2.1 - 2.3
Workbook
Lecture 12
Fri Nov 24
0800-1045 : A1-040
Lecture 13 - Review Lecture
Review and Exam Problems Final Exam 12/2016

 
Mock final exam problems in Differential Equations - Solutions
Reduced Rank Criterion (RRC)
Wed Nov 29
0900-1200
Final Exam 29/11/2017 - Solutions
Relevant material for final exam: All lectures and all exercise problems.
Fri Jan 05 2018
0900-1200
Final Exam 05/01/2018 (retake) - Solutions
Relevant material for final exam: All lectures and all exercise problems.
Fri Jan 05 2018
1500-1600
Midterm 05/01/2018 (retake) - Solutions
Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
Thu May 31 2018
1400-1500
Midterm Exam 31/05/2018 (retake)
Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
Wed Jun 20 2018
0900-1200
Final Exam 20/06/2018 (retake)
Relevant material for final exam: All lectures and all exercise problems.

Exercise sessions will take place on Mon/Tue afternoon (you can choose the session you prefer). They are weekly (except weeks with plenary sessions on Mon afternoon) starting on Tue Sep 05. Notice that the first time, both sessions are on Tue. 
Tue (weekly)
1800-1945 : C2-020
Excercise Session: Lein Mann
Own work with Problems (from the Workbook)
First session: Tue Sep 05 1800-1945 in C2-020
Most weeks thereafter: Tue 1800-1945 in C2-020
Mon (weekly)
1700-1845 : C2-020
Excercise Session: Lingzhi Yan
Own work with Problems (from the Workbook)
First session: Tue Sep 05 1800-1945 in C2-030
Most weeks thereafter: Mon 1700-1845 in C2-020