GRA6035 Mathematics - 2013/14

Syllabus

Syllabus

Reading

Current reading for GRA 6035 Mathematics:

[ME] Simon, Blume: Mathematics for Economists, International Student Edition, Norton 1994 - compulsory reading
[AP] Simon, Blume: Answers Pamphlet for Mathematics for Economists - available as pdf in It's Learning, contains solutions for [ME]
[WB] Eriksen: Digital Workbook for GRA 6035 Mathematics - available as pdf for download [last updated 11/11/13, Lecture 1-13 complete]

Some older material that could be useful:

[LSGE] Eriksen: Linear Systems and Gaussian Elimination, Handout, 2011 - available as pdf for download
[FMEA] Sydsæter, Hammond, Seierstad, Strøm: Further Mathematics for Economic Analysis, 2nd Edition, Prentice Hall 2008 - Recommended reading
Strøm, Sydsæter, Seierstad, Hammond: Student's Manual for [FMEA] - Solutions to selected problems (marked SM = Student Manual)
Eriksen, Gustavsen: GRA6035 Mathematics, Manuscript, 2009-2010 - Lecture Notes for GRA6035 Mathematics used in 2009-2010 (including Problems and Exam Problems with Solutions)

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		Workbook Lecture 2
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	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1 [FMEA] 1.2	Workbook Lecture 3
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	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9) [FMEA] 1.5 - 1.6	Workbook Lecture 4
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	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8 [FMEA] 1.7 - 1.8	Workbook Lecture 5
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		Workbook Lecture 6
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	[ME] 18.1 - 18.7, (12.3 - 12.5), 21.1 [FMEA] 3.3, 3.5	Workbook Lecture 7
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	[ME] 19.1, (19.4) [FMEA] 3.6	Workbook Lecture 8
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	[ME] 19.2 - 19.3, (19.4 - 19.6) [FMEA] 2.2 - 2.3	Workbook Lecture 9
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	[ME] 24.1 - 24.2, (24.4 - 24.6) [FMEA] 5.1 - 5.3	Workbook Lecture 10
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	[ME] 24.1 - 24.3, (24.4 - 24.6) [FMEA] 5.4 - 5.7, 6.1 - 6.4	Workbook Lecture 11
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	[ME] 23.2 [FMEA] 6.1 - 6.4, 11.1 - 11.4	Workbook Lecture 12
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.