GRA6035 Mathematics - 2015/16

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 (updated 28/09/2015; Lecture 5 has more on Markov chains)

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) in [FMEA]
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] 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 Thursday 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). There will also be a review lecture at the end of the course. In the Plenary sessions and Problem sessions we focus on problem solving. We will be working with problems from the Workbook [WB].In the Plenary Session I will solve selected problems from the Workbook. In the Problem Sessions, you may work with problems and get help.

Date:	Topic:	Reading:	Problems:
Aug 2015	FORK 1003: Linear algebra (preparatory course)
Thu Aug 20 0800-1045 : C1-020	Lecture 1 Linear systems and Gaussian Elimination	[ME] 6.1, (6.2), 7.1 - 7.4, (7.5) [LSGE] 1 - 3	[WB] Lecture 1
Mon Aug 24 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Thu Aug 27 0800-1045 : C1-020	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	[WB] Lecture 2
Mon Aug 31 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Thu Sep 03 0800-1045 : C1-020	Lecture 3 Vectors and Linear Independence	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1	WB] Lecture 3
Mon Sep 07 1700-1945 : C1-020	Plenary Session 1 We go through selected problems from Lecture 1-3 in class	Problems: 1.4, 1.8 - 1.11, 1.15, 2.18, 2.20ac, 3.4, 3.11, 3.12, 3.14, 3.15
Thu Sep 10 0800-1045 : C1-020	Lecture 4 Eigenvalues and Diagonalization	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9)	[WB] Lecture 4
Mon Sep 14 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Thu Sep 17 0800-1045 : C1-020	Lecture 5 - Note: How to compute all principal minors Markov chains. Quadratic Forms and Definiteness	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8 (Google's PageRank algorithm in more detail)	[WB] Lecture 5
Mon Sep 21 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Thu Sep 24 0800-1045 : C1-020	Lecture 6 - Note: An example Unconstrained Optimization	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	[WB] Lecture 6
Mon Sep 28 1700-1945 : C1-020	Plenary Session 2 We go through selected problems from Lecture 4-6 in class	Problems: 4.4, 4.6 - 4.12, 5.4, 5.5, 5.8, 5.9, 5.13, 6.2ii, 6.4iii, 6.5, 6.8, 6.20, 6.26
Thu Oct 01 0800-1045 : C1-020	Lecture 7 Constrained Optimization and First Order Conditions	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	[WB] Lecture 7
Mon Oct 05 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Thu Oct 08 0800-1045 : C1-020	Lecture 8 - Notes: Proof of SOC, Alternative method for NDCQ Constrained Optimization and Second Order Conditions	[ME] 19.1, (19.4)	[WB] Lecture 8
Fri Oct 09 1500-1600	Midterm exam 09/10/2015 - Solutions Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
Mon Oct 12 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Thu Oct 15 0800-1045 : C1-020	Lecture 9 - Note: Linear approximation of a function Envelope Theorems and Bordered Hessians	[ME] 19.2 - 19.3, (19.4 - 19.6)	[WB] Lecture 9
Mon Oct 19 1700-1945 : C1-020	Plenary Session 3 We go through selected problems in class	Problems: 7.1, 7.5, 7.7/8.6/9.4, 7.8/8.7, 7.9/8.8, 7.10/8.9, 8.12, 8.13, Final Exam GRA60353 Dec. 2013, Problem 4
Thu Oct 22 0800-1045 : C1-020	Lecture 10 - Notes: Review of integration First order differential equations	[ME] 24.1 - 24.2, (24.4 - 24.6)	[WB] Lecture 10
Mon Oct 26 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Mon Nov 02 1700-1945 : C2-010/045	Problem Session We work with problems from [WB]. TAs are available to help
Thu Nov 05 0800-1045 : C1-02	Lecture 11 Exact and second order linear differential equations	[ME] 24.1 - 24.3, (24.4 - 24.6)	[WB] Lecture 11
Mon Nov 09 1700-1945 : C1-020	Plenary Session 4 We go through selected problems in class	Problems: 7.4/8.3, 8.10, 8.11, 9.5, 10.12, 10.14, 10.15, 11.11, Final Exam GRA60353 Dec. 2013, Problem 3-4
Thu Nov 12 0800-1045 : C1-020	Lecture 12 Difference Equations	[ME] 23.2	[WB] Lecture 12
Thu Nov 19 0800-1045 : C1-020	Lecture 13 - Review: Matrix Problems, Unconstrained Optimization Review with Exam Problems from Final Exam GRA60353 12/2014
Tue Dec 08 1400-1645 : C1-020	Lecture 14 - Review: Constrained Optimization, Differential/Difference equations Review with Exam Problems from Final Exam GRA60353 12/2014
Fri Dec 11 0900-1200	Final exam 11/12/2015 - Solutions Relevant material for final exam: All lectures and all exercise problems.

Wed Feb 24 1700-1945 : C1-050	Retake review: Lecture 1 Linear algebra and matrices
Fri Feb 26 1400-1645 : C1-050	Retake review: Lecture 2 Differential equations
Mon Feb 29 1700-1945 : D3-090	Retake review: Lecture 3 Optimization in several variables
Fri Mar 04 1500-1800	Final exam 14/03/2016 - Solutions Relevant material for final exam: All lectures and all exercise problems.
Mon Mar 07 1800-1900	Midterm exam 07/03/2016 - Solutions Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures