GRA6035 Mathematics - 2013/14

Syllabus

Reading

Current reading for GRA 6035 Mathematics: Some older material that could be useful:

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] and [FMEA] in the Lecture Plan below is indicative of the curriculum of  the course.

Lecture Plan

The lecture plan is tentative, and may be changed/updates during the semester. In some cases, only parts of the sections indicated in the Reading column is required for this course (material in paranthese is not core material, but still useful to read to link the mathematics in the course to applications in economy and finance). Lecture notes will be uploaded as they become available (typically soon after the lecture). I have office hours Wednesday 12.00 - 14.00 in my office B4-032.It is of course not necessary to make an appointment to see me in the office hours.

There will be 13 lectures (in general, one per week). You may choose if you want to follow Lecture series A or Lecture series B. Lecture 1 is common for both lecture series, and I will inform about the differences between A and B so that you may make an informed choice. It will be possible to switch between the lecture series during the semester (or even follow both, if you want to, although that should not be necessary). Of course, the curriculum and the exams will be the same for all students in GRA 6035 Mathematics.

There will also be a number of plenary sessions and problem sessions, where we focus on problem solving. In the plenary sessions, I will go through selected problems. In the problem sessions, you will work with problems individually or in groups, and both I and a teaching assistant will be available to help you. We will be working with problems from the Workbook.
Date: Topic: Reading: Problems:
Fri Aug 23
1400-1645 : C1-020
Lecture 1
Linear systems and Gaussian Elimination
[ME] 6.1, (6.2), 7.1 - 7.4, (7.5)
[LSGE] 1 - 3, [FMEA] 1.3 - 1.4
Workbook
Lecture 1
 
  
Lecture Series A: Adapted for students who need to revise prerequisites
Lecture Series B: Adapted for students who do not need to revise prerequisites
Test of prerequisites To be used
for self-assessment of prerequisites
Tue Aug 27
1700-1945 : C1-060
Lecture 2 - Lecture Series A
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
[FMEA] 1.1, 1.9
Workbook
Lecture 2
 
Wed Aug 28
1700-1945 : C1-060
Lecture 2 - Lecture Series B
Matrices and Matrix Algebra
Thu Aug 29
0800-1045 : C1-060
Lecture 3 - Lecture Series A
Vectors and Linear Independence
[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1
[FMEA] 1.2
Workbook 
Lecture 3
Fri Aug 30
1400-1645 : C1-060
Lecture 3 - Lecture Series B
Vectors and Linear independence
Thu Sep 12
0800-1045 : C1-060
Lecture 4 - Lecture Series A
Eigenvalues and Diagonalization
[ME] 23.1 - 23.4, 23.6 -23.7, (23.9)
[FMEA] 1.5 - 1.6
Workbook 
Lecture 4
Mon Sep 16
1700-1945 : C1-060
Lecture 4 - Lecture Series B
Eigenvalues and Diagonalization
Tue Sep 17
1700-1945 : C1-000
Exercises - Plenary Session
We go through selected problems from Workbook Lecture 1-4
Problems: 1.4, 1.15, 2.18, 3.4, 3.5,
3.14, 3.15, 4.6, 4.7, 4.8, 4.9, 4.11 
Workbook
Lecture 1-4 
Thu Sep 19
0800-1045 : C1-060
Lecture 5 - Lecture Series A
Quadratic Forms and Definiteness
[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8
[FMEA] 1.7 - 1.8
Workbook 
Lecture 5
Fri Sep 20
1400-1645 : C1-060
Lecture 5 - Lecture Series B
Quadratic Forms and Definiteness
Tue Sep 24
1700-1945 : C2-010/020
Exercises - Problem Session
Note on finding eigenvalues for 3x3 matrices
Eivind Eriksen
Ledia Bano
Workbook 
Chapter 1 - 5 
Thu Sep 26
0800-1045 : C1-060
Lecture 6 - Lecture Series A - Note: Counter-example
Unconstrained Optimization
[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1
[FMEA] 3.1 - 3.2, 3.4
Workbook
Lecture 6
Fri Sep 27
1400-1645 : C1-060
Lecture 6 - Lecture Series B - Note: Counter-example
Unconstrained Optimization
Tue Oct 01
1700-1945 : C1-060
Exercises - Plenary Session
Workbook Chapter 5 - 6
Problems: 5.5, 5.7, 5.11, 6.9, 6.21,
6.27, Midterm V-2012 Problem 1-7 

 
Fri Oct 04
1400-1645 : C1-060
Lecture 7 - Lecture Series B - Note. How to sketch subsets - Note: Avoiding NDCQ
Constrained Optimization and First Order Conditions
[ME] 18.1 - 18.7, (12.3 - 12.5), 21.1
[FMEA] 3.3, 3.5
Workbook
Lecture 7
Mon Oct 07
1700-1945 : C1-060
Lecture 7 - Lecture Series A - Note. How to sketch subsets - Note: Avoiding NDCQ
Constrained Optimization and First Order Conditions
Tue Oct 08
1700-1945 : C1-060
Lecture 8 - Lecture Series B
Constrained Optimization and Second Order Conditions
[ME] 19.1, (19.4)
[FMEA] 3.6
Workbook
Lecture 8
Thu Oct 10
0800-1045 : C1-060
Lecture 8 - Lecture Series A
Constrained Optimization and Second Order Conditions
Oct 11
1500-1600
Midterm Exam 11/10/2013 - Solution
Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
Tue Oct 15
1700-1945 : C2-010/020
Exercises - Problem Session
Workbook Chapter 6 - 8
Eivind Eriksen
Ledia Bano

 
Thu Oct 17
0800-1045 : C1-060
Lecture 9 - Lecture Series A
Envelope Theorems and Bordered Hessians
[ME] 19.2 - 19.3, (19.4 - 19.6)
[FMEA] 2.2 - 2.3
Workbook 
Lecture 9
Fri Oct 18
1400-1645 : C1-060
Lecture 9 - Lecture Series B
Envelope Theorems and Bordered Hessians
Tue Oct 22
1700-1945 : C1-060
Exercises - Plenary Session
Workbook Chapter 7 - 9
Problems: 7.5, 7.6/8.6/9.4, 7.7/8.7,
7.8/8.8, 8.11, (8.12), 8.13, (9.9)

 
Thu Oct 24
0800-1045 : C1-060
Lecture 10 - Lecture Series A - Review of integration
First Order Differential Equations
[ME] 24.1 - 24.2, (24.4 - 24.6)
[FMEA] 5.1 - 5.3
Workbook
Lecture 10
Fri Oct 25
1400-1645 : C1-060
Lecture 10 - Lecture Series B - Review of integration
First Order Differential Equations
Tue Oct 29
1700-1945 : C2-010/020
Exercises - Problem Session
Workbook Chapter 9 - 10
Eivind Eriksen
Ledia Bano
Thu Oct 31
0800-1045 : C1-060
Lecture 11 - Lecture Series A
Second Order Differential Equations
[ME] 24.1 - 24.3, (24.4 - 24.6)
[FMEA] 5.4 - 5.7, 6.1 - 6.4
Workbook
Lecture 11
Fri Nov 01
1400-1645 : C1-060
Lecture 11 - Lecture Series B
Second Order Differential Equations
Tue Nov 05
1700-1945 : C2-010/020
Exercises - Problem Session
Workbook Chapter 11, Exam Problems
Eivind Eriksen
Ledia Bano
Fri Nov 08
1400-1645 : C1-060
Lecture 12 - Lecture Series B
Difference Equations
[ME] 23.2
[FMEA] 6.1 - 6.4, 11.1 - 11.4
Workbook 
Lecture 12
Tue Nov 19
1700-1945 : C1-060
Lecture 12 - Lecture Series A
Difference Equations
Thu Nov 21
0800-1045 : C1-060
Lecture 13 - Part I
Review and Exam Problems: 1) Matrix methods 2) Unconstrained ptimization
Final exam 12/2012 Problem 1-2
Final exam 12/2012 Solutions

Fri Nov 22
1400-1645 : C1-060
Lecture 13 - Part II - Note on SOC
Review and Exam Problems: 3) Constrained optimization 4) Difference/differential equations
Final exam 12/2012 Problem 3-4
Final exam 12/2012 Solutions
Mock Exam - Solutions - Note on principal minors   
Dec 13
0900-1200
Final Exam 13/12/2013 - Solution
Relevant material for final exam: All lectures and all exercise problems.
Apr 30 2014
0900-1000
Midterm Exam 30/04/2014 - Solution
Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
May 12 2014
0900-1200
Final Exam 12/05/2014 - Solution
Relevant material for final exam: All lectures and all exercise problems.