GRA6035 Mathematics - 2016/17

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

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 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). 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 25 0800-1045 : A1-040	Lecture 1 Linear systems and Gaussian Elimination	[ME] 6.1, (6.2), 7.1 - 7.4, (7.5) [LSGE] 1 - 3	Workbook Lecture 1
Tue Aug 30 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Thu Sep 01 0800-1045 : A1-040	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	Workbook Lecture 2
Tue Sep 06 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Tue Sep 13 1700-1945 : A1-040	Lecture 3 Vectors and Linear Independence	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1	Workbook Lecture 3
Thu Sep 15 0800-1045 : A1-040	Lecture 4 Eigenvalues and Diagonalization	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9)	Workbook Lecture 4
Tue Sep 20 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Thu Sep 22 0800-1045 : A1-040	Lecture 5 - Notes: How to compute all principal minors - Google's PageRank algorithm Markov chains. Quadratic Forms and Definiteness	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8 (Google's PageRank algorithm in more detail)	Workbook Lecture 5
Tue Sep 27 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Thu Sep 29 1700-1945 : A1-040	Lecture 6 Unconstrained Optimization	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	Workbook Lecture 6
Tue Oct 04 1700-1945 : A1-040	Plenary Problem Session I Review: Determinant/rank, diagonalization/Markov chains, definiteness and convex/concave functions	Problem 3.12, 4.3b, 4.10, 5.7, 5.9, 6.12, Midterm 10/2014 Pb 5,7-8, Midterm 03/2106 Pb 3,6,7, Midterm 10/2015: Pb 1-8
Thu Oct 06 0800-1045 : A1-040	Lecture 7 Constrained Optimization and First Order Conditions	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	Workbook Lecture 7
Fri Oct 07 1500-1600	Midterm exam 07/10/2016 - Solutions Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures
Tue Oct 11 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Thu Oct 13 0800-1045 : A1-040	Lecture 8 - Notes: Proof of SOC, Alternative method for NDCQ Constrained Optimization and Second Order Conditions	[ME] 19.1, (19.4)	Workbook Lecture 8
Tue Oct 18 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Thu Oct 20 0800-1045 : A1-040	Lecture 9 - Note: Linear approximation of a function Envelope Theorems and Bordered Hessians	[ME] 19.2 - 19.3, (19.4 - 19.6)	Workbook Lecture 9
Tue Oct 25 1700-1945 : A1-040	Plenary Problem Session II Lagrange/Kuhn-Tucker problems	Problem 6.1 iii), 7.1 v) - vi), 7.4/8.3, 7.6/8.5, 7.8/8.7, 7.9/8.8, 7.11/8.10, 8.12, 8.13
Thu Oct 27 0800-1045 : A1-040	Lecture 10 - Notes: Review of integration First order differential equations	[ME] 24.1 - 24.2, (24.4 - 24.6)	Workbook Lecture 10
Tue Nov 01 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Tue Nov 08 1815-2100 : A1-040	Plenary Problem Session III - Notice date/time!	Problem 8.10/7.11, 7.7/8.6/9.4, 9.5, 9.6 ii) / 9.7 ii), 9.9, 9.14
Thu Nov 10 0800-1045 : A1-040	Lecture 11 Exact and second order linear differential equations	[ME] 24.1 - 24.3, (24.4 - 24.6)	Workbook Lecture 11
Tue Nov 15 1700-1945 : A1-040	Plenary Problem Session IV	Problem 10.8 ii), 10.12, 10.14, 10.15, 11.5, 11.6 ii), 11.7, 11.8 ii), 11.9, 11.11, 11.14
Thu Nov 17 0800-1045 : A1-040	Lecture 12 Stability. Difference Equations	[ME] 23.2	Workbook Lecture 12
Mon Nov 21 1700-1945 : A1-040	Lecture 13 - Review Lecture Review with Exam Problems: Final exam 12/2015
Tue Nov 22 1700-1945 : C2-005/045/065	Exercise Session Work with problems. TAs (teaching assistants) will be present.
Thu Dec 01 0900-1200	Final Exam 01/12/2016 - Solutions - Justification of grades (common part) Relevant material for final exam: All lectures and all exercise problems.

Fri Jan 06 0900-1000	Midterm 06/01/2017 - Solutions Relevant material for midterm exam: Lecture 1-6 and Exercise problems from these lectures.
Fri Jan 06 1200-1500	Final Exam 06/01/2017 - Solutions Relevant material for final exam: All lectures and all exercise problems.

Thu May 18 0900-1000	Midterm 18/05/2017 - Solutions Relevant material for midterm exam: Lecture 1-6 and Exercise problems from these lectures.
Tue June 20 0900-1200	Final Exam 20/06/2017 - Solutions Relevant material for final exam: All lectures and all exercise problems