EBA 1180 Mathematics for Data Science

Course description for EBA 1180 Mathematics for Data Science, a core course in the BSc Data Science for Business programme. The course will cover calculus in one variable, integration, matrices and linear systems, and calculus in two variables (including optimization with or without constraints), with emphasis on applications in econmics and finance.
For material from last year's course, see EBA 1180 Mathematics for Data Science 2023/24.

Reading

[EMEA] Sydsæter, Hammond et al, Essential Mathematics for Economic Analysis, Pearson 2021 (6th ed.) - textbook.

Exams

Written exam (EBA11805) at the end of the autumn semester (3h, counts 40%), and written exam (EBA11806) at the end of the spring semester (5h, counts 60%), with grade A-F. Both exams must be passed to complete the course.
There will be re-take exams the following semester for both exams.
Previous exam problems with solutions.

Lecture plan

Lectures: Tuesday at 10-12 (D3-080) and Thursday at 12-14 (B2-040), with some exceptions (see the lecture plan below)
Exercise sessions: Thursday at 14-18 (D3-037); The lecturer and Learning Assistants will be present

Spring semester	Lecturer Kristina Rognlien Dahl (Office B3y-086); Office hours: By appointment	Reading	Problems
Tue Jan 07: 10-12, D3-080	Lecture 25: Indefinite integral and integration rules.	[EMEA] 10.1	Problem set 25
Thu Jan 09: 12-14, B2-040	Lecture 26: Substitution. Integration by parts.	[EMEA] 10.5 - 10.6	Problem set 26: Thu 14-18, D3-037
Tue Jan 14: 10-12, D3-080	Lecture 27: Review. Problems.		Problem set 27
Thu Jan 16: 12-14, B2-040	Lecture 28: Partial fractions and integration of rational functions	[EMEA] 10.6	Problem set 28: Thu 14-18, D3-037
Tue Jan 21: 10-12, D3-080	Lecture 29: Definite integrals. Improper integrals.	[EMEA] 10.2 - 10.3, 10.7	Problem set 29
Thu Jan 23: 12-14, B2-040	Lecture 30: Definite integrals and area. Economic applications.	[EMEA] 10.2, 10.4	Problem set 30: Thu 14-18, D3-037
Tue Jan 28: 10-12, D3-080	Lecture 31: Systems of equations. Linear systems.	[EMEA] 12.2, 15.10	Problem set 31
Thu Jan 30: 12-14, B2-040	Lecture 32: Gaussian elimination. Matrices and vectors.	[EMEA] 12.1, 12.3 - 12.5, 12.8 - 12.9	Problem set 32: Thu 14-18, D3-037
Tue Feb 04: 10-12, D3-080	Lecture 33: Vectors. Determinants. Cramer's rule.	[EMEA] 13.8	Problem set 33
Thu Feb 06: 12-14, B2-040	Lecture 34: Determinants and linear systems. Parameters.	[EMEA] 13.1 - 13.5	Problem set 34: Thu 14-18, D3-037
Tue Feb 11: 10-12, D3-080	Lecture 35: Linear combinations. Matrix algebra.	[EMEA] 12.6 - 12.7	Problem set 35
Thu Feb 13: 12-14, B2-040	Lecture 36: Inverse matrices. Examples.	[EMEA] 13.6 - 13.7	Problem set 36: Thu 14-18, D3-037
Tue Feb 25: 10-12, D3-080	Lecture 37: Exercises. More inverses. The dot product.	[EMEA] 12.6 - 12.7	Problem set 37
Thu Feb 27: 12-14, B2-040	Lecture 38: Functions in two variables. Partial derivation.	[EMEA] 14.1 - 14.3	Problem set 38: Thu 14-18, D3-037
Tue Mar 04: 10-12, D3-080	Lecture 39: Hessian matrices. Gradientens. Tangents of a level curve.	[EMEA] 14.6, 15.3	Problem set 39
Thu Mar 06: 12-14, B2-040	Lecture 40: Review. Linear approximations.	[EMEA] 15.8	Problem set 40: Thu 14-18, D3-037
Tue Mar 11: 10-12, D3-080	Lecture 41: Stationary points. The second derivative test.	[EMEA] 17.1 - 17.3	Problem set 41
Thu Mar 13: 12-14, B2-040	Lecture 42: Review. Problems.		Problem set 42: Thu 14-18, D3-037
Tue Mar 18: 10-12, D3-080	Lecture 43: Global max/min. Extreme value theorem.	[EMEA] 17.5	Problem set 43
Thu Mar 20: 12-14, B2-040	Lecture 44: Review. Optimization with constraints.	[EMEA] 7.6	Problem set 44: Thu 14-18, D3-037
Tue Mar 25: 10-12, D3-080	Lecture 45: Method of Lagrange multipliers.	[EMEA] 18.1	Problem set 45
Thu Mar 27: 12-14, B2-040	Lecture 46: Examples. Method of Lagrange multipliers.	[EMEA] 18.3 - 18.4	Problem set 46: Thu 14-18, D3-037
Tue Apr 01: 10-12, D3-080	Lecture 47: Interpretation of Lagrange multipliers.	[EMEA] 18.2	Problem set 47
Thu Apr 03: 12-14, B2-040	Lecture 48: Review. Problems.		Problem set 48: Thu 14-18, D3-037
Fri May 09: 09-12	Midterm exam EBA11805	All material from the autumn semester.
Wed May 23: 09-14	Final exam EBA11806	All material from the autumn and spring semester.

Autumn semester	Lecturer Runar Ile (Office B3y-087); Office hours Tuesday 12-14 (by appointment)	Reading	Problems
Wed Aug 21: 10-12, B2-030	Lecture 1: Basic algebra.	[EMEA] 2.1 - 2.5, 2.7	Problem set 1: Wednesday 12-16, CU1-067
Tue Sep 27: 10-12, B2-030	Lecture 2: Rates of change. Powers and roots. Interest.	[EMEA] 2.2, 11.1, 11.3	Problem set 2
Wed Aug 28: 10-12, B2-030	Lecture 3: Present value. Internal rate of return.	[EMEA] 11.5.1 - 11.5.4	Problem set 3: Wednesday 12-16, CU1-067
Tue Sep 03: 10-12, B2-030	Lecture 4: Review. Finite geometric series. Annuities.	[EMEA] 11.4.1 - 11.4.3, 4.9.2	Problem set 4
Wed Sep 04: 10-12, B2-030	Lecture 5: Infinite geometric series and limits. Euler's number and continuous compounding.	[EMEA] 11.4.4 - 12.4.10, 4.9.2	Problem set 5: Wednesday 12-16, CU1-067
Tue Sep 10: 10-12, B2-030	Lecture 6: Review. Linear and quadratic equations.	[EMEA] 3.1, 3.3	Problem set 6
Wed Sep 11: 10-12, B2-030	Lecture 7: Equations with parameters. Polynomial equations.	[EMEA] 3.2, 4.7	Problem set 7: Wednesday 12-16, CU1-067
Tue Sep 17: 10-12, B2-030	Lecture 8: Review. Polynomial division. Factorization.	[EMEA] 4.7	Problem set 8
Wed Sep 18: 10-12, B2-030	Lecture 9: Rational and radical equations. Inequalities.	[EMEA] 3.4 - 5, 2.6	Problem set 9: Wednesday 12-16, CU1-067
Wed Sep 25: 10-12, B2-030	Lecture 10: Functions and graphs. Linear and quadratic functions. Cost and revenue functions.	[EMEA] 4.1 - 4.6	Problem set 10: Wednesday 12-16, CU1-067
Tue Oct 01: 10-12, B2-030	Lecture 11: Review.		Problem set 11
Wed Oct 02: 10-12, B2-030	Lecture 12: Increasing and descreasing functions. Circles and ellipses. Polynomial functions.	[EMEA] 5.5, 4.7, 7.9	Problem set 12: Wednesday 12-16, CU1-067
Tue Oct 08: 10-12, B2-030	Lecture 13: Rational functions and asymptotes.	[EMEA] 7.8, 7.10, 5.2-3	Problem set 13</td>
Wed Oct 09: 10-12, B2-030	Lecture 14: Inverse functions. Exponential functions and logarithms.	[EMEA] 5.3, 4.9 - 10	Problem set 14: Wednesday 12-16, CU1-067
Tue Oct 15: 10-12, B2-030	Lecture 15: Review.		Problem set 15
Wed Oct 16: 10-12, B2-030	Lecture 16: Tangents. Differentiation and rules for differentiation.	[EMEA] 6.1, 6.6-8, 6.10-11	Problem set 16: Wednesday 12-16, CU1-067
Tue Oct 22: 10-12, B2-030	Lecture 17: Review. Stationary point and extreme points.	[EMEA] 9.1-2, 6.3	Problem set 17
Wed Oct 23: 10-12, B2-030	Lecture 18: Optimization in one variable.	[EMEA] 9.4, 9.6	Problem set 18: Wednesday 12-16, CU1-067
Tue Oct 29: 10-12, B2-030	Lecture 19: Review. Implicit differentiation.	[EMEA] 7.1	Problem set 19
Wed Oct 30: 10-12, B2-030	Lecture 20: Second order derivatives. Convex and concave functions.	[EMEA] 6.9, 9.6, 8.5-6	Problem set 20: Wednesday 12-16, CU1-067
Tue Nov 05: 10-12, B2-030	Lecture 21: Review. l'Hôspital's rule.	[EMEA] 7.12	Problem set 21
Wed Nov 06: 10-12, B2-030	Lecture 22: Marginal cost and revenue. Average unit cost, cost optimum.	[EMEA] 6.4, 9.3, 9.5	Problem set 22: Wednesday 12-16, CU1-067
Tue Nov 12: 10-12, B2-030	Lecture 23: Review. Elasticity.	[EMEA] 7.7	Problem set 23
Wed Nov 13: 10-12, B2-030	Lecture 24: Linearisation. Taylor polynomials.	[EMEA] 7.4 - 7.5	Problem set 24: Wednesday 12-16, CU1-067
Wed Nov 20: 12-16, CU1-067	Tutoring (no lecture)

Fri Dec 06: 09-12	Midterm exam EBA11805 - Solutions
Thu Dec 19: 09-14	Final exam EBA11806 - Solutions (retake)