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 16 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.
Date:  Topic:  Reading:  Problems: 
Fri Aug 23 14001645 : C1020 
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 selfassessment of prerequisites 

Tue Aug 27 17001945 : C1060 
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 17001945 : C1060 
Lecture
2  Lecture Series B Matrices and Matrix Algebra 

Thu Aug 29 08001045 : C1060 
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 14001645 : C1060 
Lecture
3  Lecture Series B Vectors and Linear independence 

Thu Sep 12 08001045 : C1060 
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 17001945 : C1060 
Lecture
4  Lecture Series B Eigenvalues and Diagonalization 

Tue Sep 17 17001945 : C1000 
Exercises
 Plenary Session We go through selected problems from Workbook Lecture 14 
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 14 
Thu Sep 19 08001045 : C1060 
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 14001645 : C1060 
Lecture
5  Lecture Series B Quadratic Forms and Definiteness 

Tue Sep 24 17001945 : C2010/020 
Exercises
 Problem Session Note on finding eigenvalues for 3x3 matrices 
Eivind Eriksen Ledia Bano 
Workbook Chapter 1  5 
Thu Sep 26 08001045 : C1060 
Lecture
6  Lecture Series A  Note: Counterexample 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 14001645 : C1060 
Lecture
6  Lecture Series B  Note: Counterexample Unconstrained Optimization 

Tue Oct 01 17001945 : C1060 
Exercises
 Plenary Session Workbook Chapter 5  6 
Problems: 5.5, 5.7, 5.11, 6.9, 6.21, 6.27, Midterm V2012 Problem 17 

Fri Oct 04 14001645 : C1060 
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 17001945 : C1060  Lecture
7  Lecture Series A  Note. How to sketch subsets  Note: Avoiding NDCQ Constrained Optimization and First Order Conditions  
Tue Oct 08 17001945 : C1060 
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 08001045 : C1060 
Lecture
8  Lecture Series A Constrained Optimization and Second Order Conditions 

Oct
11 15001600 
Midterm Exam 11/10/2013  Solution Relevant material for Midterm: Lecture 16 and Exercise problems from these lectures 

Tue Oct 15 17001945 : C2010/020 
Exercises
 Problem Session Workbook Chapter 6  8 
Eivind Eriksen Ledia Bano 

Thu Oct 17 08001045 : C1060 
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 14001645 : C1060 
Lecture
9  Lecture Series B Envelope Theorems and Bordered Hessians 

Tue Oct 22 17001945 : C1060 
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 08001045 : C1060 
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 14001645 : C1060 
Lecture
10  Lecture Series B  Review of integration First Order Differential Equations 

Tue Oct 29 17001945 : C2010/020 
Exercises
 Problem Session Workbook Chapter 9  10 
Eivind Eriksen Ledia Bano 

Thu Oct 31 08001045 : C1060 
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 14001645 : C1060 
Lecture
11  Lecture Series B Second Order Differential Equations 

Tue Nov 05 17001945 : C2010/020 
Exercises
 Problem Session Workbook Chapter 11, Exam Problems 
Eivind Eriksen Ledia Bano 

Fri Nov 08 14001645 : C1060 
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 17001945 : C1060  Lecture
12  Lecture Series A Difference Equations  
Thu Nov 21 08001045 : C1060 
Lecture
13  Part I Review and Exam Problems: 1) Matrix methods 2) Unconstrained ptimization 
Final exam 12/2012 Problem 12 Final exam 12/2012 Solutions 

Fri Nov 22 14001645 : C1060 
Lecture
13  Part II  Note on SOC Review and Exam Problems: 3) Constrained optimization 4) Difference/differential equations  Final exam 12/2012 Problem 34 Final exam 12/2012 Solutions 

Mock Exam  Solutions  Note on principal minors  
Dec
13 09001200 
Final Exam 13/12/2013  Solution Relevant material for final exam: All lectures and all exercise problems. 

Apr 30 2014 09001000  Midterm Exam 30/04/2014  Solution Relevant material for Midterm: Lecture 16 and Exercise problems from these lectures  
May 12 2014 09001200  Final Exam 12/05/2014  Solution Relevant material for final exam: All lectures and all exercise problems. 