- GRA 6035 Mathematics - All academic years, with exams/solutions

- [ME] Simon, Blume: Mathematics for Economists, International Student Edition, Norton 1994. Textbook for GRA6035 Mathematics, compulsory reading.
- [ODE] Eriksen: Differential
Equations - Solutions to problems. Final version uploaded Nov 09 2017.

- [WB] Eriksen: Digital Workbook for GRA 6035 Mathematics. Workbook with problems and solutions, including links to exam problems, updated on Nov 07, 2017 - Solution to Avanced matrix problems (Workbook, Lecture 4)

- [AP] Simon, Blume: Answers Pamphlet for Mathematics for Economists. Available as pdf in It's Learning, contains solutions for problems in the textbook [ME].
- [LSGE] Eriksen: Linear Systems and Gaussian Elimination, Handout, 2011. Available as pdf for download, covers part of the course, which is also covered in the textbook [ME].
- [M] Eriksen: Matematikk for økonomi og finans, Cappelen Damm 2016 (in norwegian). Textbook for the mathematics course at BSc/undergraduate level at BI, covers the material from the preparatory course FORK 1003.
- [FMEA] Sydsæter, Hammond, Seierstad, Strøm: Further Mathematics for Economic Analysis, 2nd Edition, Prentice Hall 2008. Recommended reading, used at textbook in GRA 6035 Mathematics earlier.
- Strøm, Sydsæter, Seierstad, Hammond: Student's Manual for [FMEA]. Solutions to selected problems (marked SM = Student Manual) in [FMEA].
- Eriksen, Gustavsen: GRA6035 Mathematics. Available as pdf for download. 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.

In the office hours, you can ask me for help with problems or ask other questions from the lectures. It is not necessary to make an appointment to see me in the office hours. It is often possible to see me outside office hours (come by to see if I am available, or make an appointment). I will be in my office most of the time Mon-Fri, except Thu 08-11 when I teach another course.

The lecture plan is tentative, and may be changed/updated during the semester. In some cases, only parts of the sections indicated in the Reading column is required for this course (material in parantheses is not core material, but still useful to read to link the mathematics in the course to applications). Lecture notes will be uploaded as they become available (typically soon after the lecture).

Date: | Topic: | Reading: | Problems: |

Aug 2017 | FORK 1003: Mathematics module (preparatory course) | ||

Fri Aug 25 0800-1045 : A1-040 |
Lecture
1 Linear systems and Gaussian Elimination. Rank. |
[ME] 6.1, (6.2), 7.1 - 7.4, (7.5) [LSGE] 1 - 3 |
Workbook
Lecture 1 |

Fri 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 05 1800-1945 : C2-020/030 | First Excercise Session Problems from Lecture 1-2 | ||

Fri Sep 08 0800-1045 : A1-040 |
Lecture
3 Vectors and Linear Independence |
[ME] 10.1 - 10.3, (10.4 - 10.7),
11.1 |
Workbook
Lecture 3 |

Fri 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 |

Mon Sep 18 1700-1945 : A1-040 | Plenary Session 1 Problems from Lecture 1-4 + [ODE] Integration | Workbook 1.15, 2.18b, 3.12, 3.14, 4.5, 4.9, 4.10, 4.11, 4.12 Midterm Exams 10/2016 Pb 1, 10/2014 Pb 3, 03/2016 Pb 3, 10/2015 Pb 4 | |

Fri Sep 22 0800-1045 : A1-040 |
Lecture 5
- Notes: How to
compute all principal minors Markov chains. Quadratic Forms and Definiteness |
[ME] 13.1
- 13.5,
16.1 - 16.4, 23.8 Application of eigenvectors: Google's PageRank algorithm |
Workbook Lecture 5 |

Fri Sep 29 1700-1945 : A1-040 |
Lecture 6 - New result on semidefiniteness Unconstrained Optimization |
[ME] 14.1
- 14.4,
14.8, 17.1 - 17.5, 30.1 |
Workbook Lecture 6 |

Fri 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 |

Mon Oct 09 1700-1945 : A1-040 | Plenary Session 2 Problems from Lecture 4-6 + Midterm Exam 10/2016 | Workbook: 4.3b, 4.10, 5.9, 5.15, 6.1c, 6.12 Midterm 10/2016 Problem 1-8, Midterm 03/2016 Problem 5,7,8 | |

Fri 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 |

Fri Oct 13 1500-1600 |
Midterm
exam 13/10/2017 - Solution Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures |
||

Fri Oct 20 0800-1045 : A1-040 |
Lecture
9 Envelope Theorems and Bordered Hessians |
[ME] 19.2 - 19.3,
(19.4 - 19.6) |
Workbook Lecture 9 |

Fri Oct 27 0800-1045 : A1-040 |
Lecture 10 First order differential equations |
[ME] 24.1 - 24.2, (24.4 - 24.6) [ODE] Differential Equations 1.1 - 1.7 |
Workbook
Lecture 10 |

Mon Oct 30 1700-1945 : A1-040 | Plenary Session 3 Problems from Lecture 7-9 | Workbook 7.1, 7.8/8.7, 7.11/8.10, 8.13, 8.8, 8.12 Exam 12/2015 Problem 3-4 Exam 01/2017 Problem 3-4 | |

Fri Nov 10 0800-1045 : A1-040 |
Lecture
11 Stability. Second order differential equations. Systems of differential equations. |
[ME] 24.1 - 24.3,
(24.4 - 24.6) [ODE] Differential Equations 1.8 - 1-10, 2.1 - 2.2 |
Workbook Lecture 11 |

Mon Nov 13 1700-1945 :A1-040 | Plenary Session 4 Problems from Lecture 10-11 | Workbook 10.8, 10.12, 10.15, 11.6, 11.11 [ODE] Differential
Equations 1.14, 1.24, 2.3 Exam 01/2017 Problem 2 | |

Fri Nov 17 0800-1045 : A1-040 |
Lecture
12 Systems of differential equations. Difference Equations. |
[ME]
23.2 [ODE] Differential Equations 2.1 - 2.3 |
Workbook
Lecture 12 |

Fri Nov 24 0800-1045 : A1-040 |
Lecture 13
- Review Lecture Review and Exam Problems Final Exam 12/2016 |
||

Mock final exam problems in Differential Equations - Solutions Reduced Rank Criterion (RRC) | |||

Wed Nov 29 0900-1200 |
Final
Exam 29/11/2017 - Solutions Relevant material for final exam: All lectures and all exercise problems. |
||

Fri Jan 05 2018 0900-1200 |
Final
Exam 05/01/2018 (retake) - Solutions Relevant material for final exam: All lectures and all exercise problems. |
||

Fri Jan 05 2018 1500-1600 | Midterm
05/01/2018 (retake) - Solutions Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures | ||

Thu May 31 2018 1400-1500 | Midterm Exam 31/05/2018 (retake) Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures | ||

Wed Jun 20 2018 0900-1200 | Final Exam 20/06/2018 (retake) Relevant material for final exam: All lectures and all exercise problems. |

Exercise sessions will take place on Mon/Tue afternoon (you can choose the session you prefer). They are weekly (except weeks with plenary sessions on Mon afternoon) starting on Tue Sep 05. Notice that the first time, both sessions are on Tue.

Tue (weekly) 1800-1945 : C2-020 |
Excercise Session: Lein Mann Own work with Problems (from the Workbook) | First session: Tue Sep 05 1800-1945 in C2-020 Most weeks thereafter: Tue 1800-1945 in C2-020 |

Mon (weekly) 1700-1845 : C2-020 | Excercise Session: Lingzhi Yan Own work with Problems (from the Workbook) | First session: Tue Sep 05 1800-1945 in C2-030 Most weeks thereafter: Mon 1700-1845 in C2-020 |