Mathematics for Doctoral Economics I, 7.5 credits
Mathematics for Doctoral Economics I, 7,5 högskolepoäng
Course Syllabus for students Autumn 2020
Course Code: FJMD139
Confirmed by: Research Board Jun 12, 2019
Valid From: Autumn 2019
Version: 1
Education Cycle: Third-cycle level
Research subject: Economics


The Mathematics for Doctoral Economics I course is designed to help students be prepared for the
mathematical material typically found in the economics (especially microeconomics) and statistics courses
associated with doctoral programme in economics.

Intended Learning Outcomes (ILO)

On completion of the course, the students will be able to:

Knowledge and understanding

Skills and abilities

Judgement and approach


(i) constrained optimization with inequality constraints
(ii) the envelope theorem
(iii) calculus rules involving logs and exponentials
(iv) addition, multiplication, and inversion of matrices; vector spaces; solving sets of simultaneous
equations using matrices; and eigenvalues and eigenvectors
(v) unconstrained and constrained multivariable optimization
(vi) Taylor series expansion
(vii) the derivation of statistical functions and measures from continuous probability density functions
(viii) concavity, convexity, quasi-concavity, and quasi-convexity characteristics of functions
(ix) topological definitions and theorems, in particular fixed point theorems

Type of instruction

Lectures and homework assignments.

The teaching is conducted in English.


Admitted to a doctoral programme in economics or a related subject of a recognized business school or

Examination and grades

The course is graded Fail (U) or Pass (G).

The examination consists of three written examinations, with their contributions to the final overall grade
noted in parentheses below:
• Midterm examination (20%), which covers ILOs 1, 4, 5, 9, 10
• Final examination (80%), which covers ILOs 1, 2, 3, 6, 7, 8, 10
To pass the course the student needs to achieve at least 60% correct of the maximum possible points on
the final overall grade.

Course evaluation

A course evaluation will be conducted at the end of the course.

Other information

The course language is English.

Course literature

The primary textbook is Chiang, Alpha C. and Wainwright, Kevin C. (2005) Fundamental Methods of
Mathematical Economics 4th edition, McGraw Hill [ISBN: 007-123823-9]
The course also uses material from Sydsaeter, K., Hammond, P., Seierstad, A. and A. Strom (2008) Further
Mathematics for Economic Analysis, 2nd ed, Pearson [ISBN: 978-0-273-71328-9], including chapters 13 and 14,
and Appendix A.
Supplementary material may also be assigned.