GRA6035 Mathematics - 2014/15

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 (last updated Nov 10th 2014)

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. It is often possible to see me at my office outside office hours (come by to see if I am available, or make an appointment).

There will be 12 lectures (in general, one per week, but there are some exceptions because of scheduling issues). There will also be a number of review lectures and problem sessions. In problem sessions we focus on problem solving. We will be working with problems from the Workbook.

Date:	Topic:	Reading:	Problems:
Thu Aug 21 0800-1045 : C1-060	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
Thu Aug 28 0800-1045 : C1-060	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 [FMEA] 1.1, 1.9	Workbook Lecture 2
Mon Sep 01 1700-1945 : C2-020/045	Problem Session Lecturer + TAs
Thu Sep 04 0800-1045 : C1-000	Lecture 3B (B = Business except major in finance) Vectors and Linear Independence	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1 [FMEA] 1.2	Workbook Lecture 3
Mon Sep 08 0800-1045 : C1-060	Lecture 3F (F = Financial Economics + Business with major in finance) Vectors and Linear Independence	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1 [FMEA] 1.2	Workbook Lecture 3
Mon Sep 08 1700-1945 : C2-010/20/45	Problem Session TAs
Thu Sep 11 0800-1045 : C1-060	Lecture 4B Eigenvalues and Diagonalization	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9) [FMEA] 1.5 - 1.6	Workbook Lecture 4
Mon Sep 15 0800-1045 : C1-060	Lecture 4F Eigenvalues and Diagonalization	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9) [FMEA] 1.5 - 1.6	Workbook Lecture 4
Mon Sep 15 1700-1945 :C2-020/45, B2-070	Problem Session TAs
Thu Sep 18 0800-1045 : C1-060	Lecture 5B - Note: How to compute all principal minors Quadratic Forms and Definiteness	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8 [FMEA] 1.7 - 1.8	Workbook Lecture 5
Mon Sep 22 0800-1045 : C1-060	Lecture 5F - Note: How to compute all principal minors Quadratic Forms and Definiteness	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8 [FMEA] 1.7 - 1.8	Workbook Lecture 5
Mon Sep 22 1700-1945 : C1-060	Plenary Session - Note: How to compute eigenvalues Selected problems from Lecture 1-4	Problems: 1.4, 1.15, 2.18, 2.20c, 3.4, 3.5, 3.14, 3.15, 4.6, 4.7, 4.8, 4.9, 4.11
Thu Sep 25 0800-1045 : C1-060	Lecture 6B - Note: An 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
Mon Sep 29 0800-1045 : C1-060	Lecture 6F - Note: An 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
Mon Sep 29 1700-1945 : C2-010/20/45	Problem Session TAs
Thu Oct 02 0800-1045 : C1-060	Lecture 7B Constrained Optimization and First Order Conditions	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1 [FMEA] 3.1 - 3.2, 3.4	Workbook Lecture 7
Mon Oct 06 0800-1045 : C1-060	Lecture 7F Constrained Optimization and First Order Conditions	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1 [FMEA] 3.1 - 3.2, 3.4	Workbook Lecture 7
Mon Oct 06 1700-1945 : C2-010/20/45	Problem Session Lecturer + TAs
Thu Oct 09 0800-1045 : C1-060	Lecture 8B - Notes: Proof of SOC, Alternative method for NDCQ Constrained Optimization and Second Order Conditions	[ME] 19.1, (19.4) [FMEA] 3.6	Workbook Lecture 8
Fri Oct 10 1500-1600	Midterm exam 10/10/2014 - Solutions Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
Mon Oct 13 0800-1045 : C1-010	Lecture 8F - Notes: Proof of SOC, Alternative method for NDCQ Constrained Optimization and Second Order Conditions	[ME] 19.1, (19.4) [FMEA] 3.6	Workbook Lecture 8
Mon Oct 13 1700-1945 : C1-060	Plenary Session Selected problems from Lecture 5-8	Problems: 5.5, 6.8, 6.20, 6.26, 7.7, 7.8, 7.9, 7.10, 8.6, 8.7, 8.8, 8.9, 8.13
Thu Oct 16 0800-1045 : C1-060	Lecture 9B Envelope Theorems and Bordered Hessians	[ME] 19.2 - 19.3, (19.4 - 19.6) [FMEA] 2.2 - 2.3	Workbook Lecture 9
Mon Oct 20 0800-1045 : C1-060	Lecture 9F Envelope Theorems and Bordered Hessians	[ME] 19.2 - 19.3, (19.4 - 19.6) [FMEA] 2.2 - 2.3	Workbook Lecture 9
Mon Oct 20 1700-1945 : C2-010/20/45	Problem Session TAs
Mon Oct 27 1700-1945 : C1-050	Lecture 10F (Pål Lauritzen) - Notes: Review of integration First Order Differential Equations	[ME] 24.1 - 24.2, (24.4 - 24.6) [FMEA] 5.1 - 5.3	Workbook Lecture 10
Mon Oct 27 1700-1945 : C2-010/20/45	Problem Session TAs
Thu Oct 30 0800-1045 : C1-060	Lecture 10B - Notes: Review of integration First Order Differential Equations	[ME] 24.1 - 24.2, (24.4 - 24.6) [FMEA] 5.1 - 5.3	Workbook Lecture 10
Mon Nov 03 0800-1045 : C1-060	Lecture 11F 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
Mon Nov 03 1700-1945 : C2-010/20/45	Problem Session TAs
Thu Nov 06 0800-1045 : C1-060	Lecture 11B 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
Mon Nov 10 0800-1045 : C1-060	Lecture 12F Difference Equations	[ME] 23.2 [FMEA] 6.1 - 6.4, 11.1 - 11.4	Workbook Lecture 12
Mon Nov 10 1700-1945 : C2-010/20/45	Problem Session TAs
Thu Nov 13 0800-1045 : C1-060	Lecture 12B Difference Equations	[ME] 23.2 [FMEA] 6.1 - 6.4, 11.1 - 11.4	Workbook Lecture 12
Mon Nov 17 1700-1945 : C1-010	Lecture 13 Part I: Review with Exam Problems 1) Matrix methods 2) Unconstrained optimization	Final exam 12/2013 Problem 1-2 Final exam 12/2013 Solutions
Thu Nov 20 0800-1045 : A1-040	Lecture 13 Part II: Review with Exam Problems 3) Constrained optimization 4) Difference/differential equations	Final exam 12/2013 Problem 3-4 Final exam 12/2013 Solutions
Dec 12 0900-1200	Final exam 12/12/2014 - Solutions Relevant material for final exam: All lectures and all exercise problems.

Apr 27, 2015 0900-1000	Midterm exam 27/04/2015 - Solutions Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
May 15, 2015 0900-1200	Final exam 15/05/2015 - Solutions Relevant material for final exam: All lectures and all exercise problems.