# 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 emphasize on applications in econmics and finance. - For material from last year's course, see EBA 1180 Mathematics for Data Science 2022/23.

### Reading

- [EMEA] SydsĂ¦ter, 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 (B2-030) and Thursday at 10-12 (B2-030), with some exceptions (see the lecture plan below)**Exercise sessions**: Thursday at 12-15 (B2-065); The lecturer and Learning Assistants will be present

Spring semester | Lecturer Kristina Rognlien Dahl (Office B3y-086); Office hours TBA | Reading | Problems |
---|---|---|---|

Tue Jan 09: 10-12, B2-030 | Lecture 25: Indefinite integral and integration rules. | [EMEA] 10.1 | Problem set 25 |

Thu Jan 11: 10-12, B2-030 | Lecture 26: Substitution. Integration by parts. | [EMEA] 10.5 - 10.6 | Problem set 26: Thu 12-15, B2-065 |

Tue Jan 16: 10-12, B2-030 | Lecture 27: Review. Problems. | Problem set 27 | |

Thu Jan 18: 10-12, B2-030 | Lecture 28: Partial fractions and integration of rational functions - Part 2 | [EMEA] 10.6 | Problem set 28: Thu 12-15, B2-065 |

Tue Jan 23: 10-12, B2-030 | Lecture 29: Definite integrals. Improper integrals. | [EMEA] 10.2 - 10.3, 10.7 | Problem set 29 |

Thu Jan 25: 10-12, B2-030 | Lecture 30: Definite integrals and area. Economic applications. - Part 2 | [EMEA] 10.2, 10.4 | Problem set 30: Thu 12-15, B2-065 |

Thu Feb 01: 10-12, B2-030 | Lecture 31: Systems of equations. Linear systems and Gaussian elimination. | [EMEA] 12.2, 15.10 | Problem set 31: Thu 12-15, B2-065 |

Tue Feb 06: 10-12, B2-030 | Lecture 32: Free variables. Number of solutions of linear systems. Vectors. | [EMEA] 12.1, 12.3 - 12.5, 12.8 - 12.9 | Problem set 32 |

Thu Feb 08: 10-12, B2-030 | Lecture 33: Vectors. Determinants and linear systems. Cramer's rule. | [EMEA] 13.1 - 13.5 | Problem set 33: Thu 12-15, B2-065 |

Tue Feb 13: 10-12, B2-030 | Lecture 34: Determinants and linear systems. Problems. - Part 2 | [EMEA] 13.8 | Problem set 34 |

Thu Feb 15: 10-12, B2-030 | Lecture 35: Vector equations. Matrix multiplication. The transpose. | [EMEA] 13.6 - 13.7 | Problem set 35: Thu 12-15, B2-085 |

Tue Feb 20: 10-12, B2-030 | Lecture 36: Review. Problems. | Problem set 36 | |

Thu Feb 22: 10-12, B2-030 | Lecture 37: Computing inverse matrices. Problems. | [EMEA] 12.6 - 12.7 | Problem set 37: Thu 12-15, D3-080 |

Tue Feb 27: 10-12, B2-030 | Lecture 38: Functions in two variables. Partial derivation. | [EMEA] 14.1 - 14.3 | Problem set 38 |

Thu Feb 29: 10-12, B2-030 | Lecture 39: Hessian matrices. Gradientens. Tangents of a level curve. | [EMEA] 14.6, 15.3 | Problem set 39: Thu 12-15, B2-085 |

Tue Mar 05: 10-12, B2-030 | Lecture 40: Review. Linear approximations. | [EMEA] 15.8 | Problem set 40 |

Thu Mar 07: 10-12, B2-030 | Lecture 41: Stationary points. The second derivative test. | [EMEA] 17.1 - 17.3 | Problem set 41: Thu 12-15, B2-065 |

Mar 04 - 11 | Course paper EBA11801 (last resit) | ||

Tue Mar 12: 10-12, B2-030 | Lecture 42: Review. Problems. | Problem set 42 | |

Thu Mar 14: 10-12, B2-030 | Lecture 43: Global max/min. Extreme value theorem. | [EMEA] 17.5 | Problem set 43: Thu 12-15, B2-065 |

Tue Mar 19: 10-12, B2-030 | Lecture 44: Review. Optimization with constraints. | [EMEA] 7.6 | Problem set 44 |

Mar 13 - 20 | Course paper EBA11803 (last resit) | ||

Thu Mar 21: 10-12, B2-030 | Lecture 45: Method of Lagrange multipliers. | [EMEA] 18.1 | Problem set 45: Thu 12-15, B2-065 |

Thu Apr 04: 10-12, B2-030 | Lecture 46: Examples. Method of Lagrange multipliers. | [EMEA] 18.3 - 18.4 | Problem set 46: Thu 12-15, B2-065 |

Thu Apr 11: 10-12, B2-030 | Lecture 47: Interpretation of Lagrange multipliers. - Part 2 | [EMEA] 18.2 | Problem set 47: Thu 12-15, B2-065 |

Thu Apr 18: 10-12, B2-030 | Lecture 48: Review. Problems. | Problem set 48: Thu 12-15, B2-065 | |

Thu Apr 25 | Extra exercise session with exam problems | Problem set 49: Thu 12-15, B2-065 | |

Fri May 16: 09-12 | Midterm exam EBA11805 / EBA11802 - Solutions | All material from the autumn semester. | |

Thu May 23: 10-12, B2-010 | Lecture 49: Review lecture | ||

Wed May 27: 09-14 | Final exam EBA11806 / EBA11804 - Solutions | All material from the autumn and spring semester. | |

Autumn semester | Lecturer Runar Ile (Office B3y-087); Office hours Tue 12-14 (by appointment) | Reading | Problems |

Wed Aug 23: 10-12, B2-040 | Lecture 1: Basic algebra. | [EMEA] 2.1 - 2.5, 2.7 | Problem set 1: Wednesday 12-17, D1-065 |

Tue Aug 29: 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 30: 10-12, B2-040 | Lecture 3: Present value of cash flows. Internal rate of return. | [EMEA] 11.5.1 - 11.5.4 | Problem set 3: Wednesday 12-17, D1-065 |

Tue Sep 05: 10-12, B2-030 | Lecture 4: Review. Finite geometric series. Annuities. | [EMEA] 11.4.1 - 11.4.3, 6.11.4, 11.2, 11.3.2 | Problem set 4 |

Wed Sep 06: 10-12, B2-040 | Lecture 5: Infinite geometric series and limits. Euler's number and continuous compounding. | [EMEA] 11.4.4 - 11.4.10, 4.9.2, 6.11.4, 11.2, 11.3.2 | Problem set 5: Wednesday 12-17, D1-065 |

Tue Sep 12: 10-12, B2-030 | Lecture 6: Review. Linear and quadratic equations. | [EMEA] 3.1, 3.3 | Problem set 6 |

Wed Sep 13: 10-12, B2-040 | Lecture 7: Equations with parameters. Polynomial equations. | [EMEA] 3.2, 4.7 | Problem set 7: Wednesday 12-17, D1-065 |

Tue Sep 19: 10-12, B2-030 | Lecture 8: Review. Polynomial division. Factorization. | [EMEA] 4.7 | Problem set 8 |

Wed Sep 20: 10-12, B2-040 | Lecture 9: Rational and radical equations. Inequalities. | [EMEA] 3.4 - 3.5, 2.6 | Problem set 9: Wednesday 12-17, D1-065 |

Wed Sep 27: 10-12, B2-040 | Lecture 10: Functions and graphs. Linear and quadratic functions. Profit functions. | [EMEA] 4.1 - 4.6 | Problem set 10: Wednesday 12-17, D1-065 |

Tue Oct 03: 10-12, B2-030 | Lecture 11: Review. | Problem set 11 | |

Wed Oct 04: 10-12, B2-040 | Lecture 12: Increasing/decreasing functions. Circles. Ellipses. Polynomial functions. | [EMEA] 6.3.1 - 6.3.3, 5.4 - 5.5, 4.7, 7.9 | Problem set 12: Wednesday 12-17, D1-065 |

Tue Oct 10: 10-12, B2-030 | Lecture 13: Rational functions and asymptotes. | [EMEA] 7.8, 7.10, 5.2 - 5.3 | Problem set 13 |

Wed Oct 11: 10-12, B2-040 | Lecture 14: Inverse functions. Exponential functions. Logarithms. | [EMEA] 4.9 - 4.10 | Problem set 14: Wednesday 12-17, D1-065 |

Tue Oct 17: 10-12, B2-030 | Lecture 15: Review. | Problem set 15 | |

Wed Oct 18: 10-12, B2-040 | Lecture 16: Tangents, differentiation and rules for differentiation. | [EMEA] 6.1 - 6.2, 6.6 - 6.8, 6.10 - 6.11 | Problem set 16: Wednesday 12-17, D1-065 |

Tue Oct 24: 10-12, B2-030 | Lecture 17: Review. Stationary (critical) points and extreme points. | [EMEA] 9.1 - 9.2, 6.3 | Problem set 17 |

Wed Oct 25: 10-12, B2-040 | Lecture 18: Optimization in one variable. | [EMEA] 9.4, 9.6 | Problem set 18: Wednesday 12-17, D1-065 |

Mon Oct 30: 1200 | Course paper EBA11801 (retake) | ||

Tue Oct 31: 10-12, B2-030 | Lecture 19: Review. Implicit differentiation. | [EMEA] 7.1 | Problem set 19 |

Wed Nov 01: 10-12, B2-040 | Lecture 20: Second order derivatives. Convex and concave functions. | [EMEA] 6.9, 9.6, 8.5 - 8.6 | Problem set 20: Wednesday 12-17, D1-065 |

Tue Nov 07: 10-12, B2-030 | Lecture 21: Review. L'Hôspital's rule. | [EMEA] 7.12 | Problem set 21 |

Wed Nov 08: 10-12, B2-040 | Lecture 22: Marginal cost and revenue. Average unit cost. Cost optimum. | [EMEA] 6.4, 9.3, 9.5 | Problem set 22: Wednesday 12-17, B2-085 |

Fre Nov 10: 1200 | Course paper EBA11803 (retake) | ||

Tue Nov 14: 10-12, B2-030 | Lecture 23: Review. Elasticity. | [EMEA] 7.7 | Problem set 23 |

Wed Nov 15: 10-12, B2-040 | Lecture 24: Linearisation. Taylor polynomials. | [EMEA] 7.4 - 7.5 | Problem set 24: Wednesday 12-17, D1-065 |

Tue Dec 12: 14-17 | Midterm exam EBA11805 - Solutions - Results | ||

Mon Dec 18: 09-14 | Final exam EBA11804 (retake) - Solutions | ||