# 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. - From the 2022/23 academic year, EBA1180 Mathematics for Data Science is the new name for EBA2910 Mathematics for Business Analytics (2018-2021); The program BSc Business Analytics also changes name to BSc Data Science for Business.
- For material from last year's course, see EBA 2910 Mathematics for Business Analytics 2020/21.

### Reading

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

### Exams

- Two
**course papers**(to be handed in individually), one in the autumn and one in the spring semester, grade pass/fail. Both must be passed to complete the course. **Written exam**at the end of the autumn semester (3h, counts 20%), and**written exam**at the end of the spring semester (5h, counts 80%), with grade A-F. Both exams must be passed to complete the course.- There will be re-take exams the following semester for all exams.
- Previous exam problems with solutions.

### Lecture plan

**Lectures**: Tuesday at 10-12 (B2-060) and Tuesday at 10-12 (B2-060), with some exceptions (see the lecture plan below)**Exercise sessions**: Thursday at 12-15 (B2-080); The lecturer and Learning Assistants will be present

Spring semester (preliminary plan) | Lecturer Kristina Rognlien Dahl (Office B4-030); Office hours TBA | Reading | Problems |
---|---|---|---|

Tue Jan 10: 10-12, B2-060 | Lecture 25: Indefinite integral and integration rules. | [EMEA] 10.1 | Problem set 25 |

Thu Jan 12: 10-12, B2-060 | Lecture 26: Substitution. Integration by parts. | [EMEA] 10.5 - 10.6 | Problem set 26: Thu 12-14, B2-080 |

Tue Jan 17: 10-12, B2-060 | Lecture 27: Review. Problems. | Problem set 27 | |

Thu Jan 19: 10-12, B2-060 | Lecture 28: Partial fractions and integration of rational functions. | [EMEA] 10.6 | Problem set 28: Thu 12-14, B2-080 |

Tue Jan 24: 10-12, B2-060 | Lecture 29: Definite integrals. Improper integrals. | [EMEA] 10.2 - 10.3, 10.7 | Problem set 29 |

Thu Jan 26: 10-12, B2-060 | Lecture 30: Definite integrals and area. Economic applications. | [EMEA] 10.2, 10.4 | Problem set 30: Thu 12-14, B2-080 |

Tue Jan 31: 10-12, B2-060 | |||

Thu Feb 02: 10-12, B2-060 | Lecture 31: Systems of equations. Linear systems. | [EMEA] 12.2, 15.10 | Problem set 31: Thu 12-14, B2-080 |

Tue Feb 07: 10-12, B2-060 | Lecture 32: Gaussian elimination. Matrices and vectors. | [EMEA] 12.1, 12.3 - 12.5, 12.8 - 12.9 | Problem set 32 |

Thu Feb 09: 10-12, B2-060 | Lecture 33: Determinants and linear systems. | [EMEA] 13.1 - 13.5 | Problem set 33: Thu 12-14, B2-080 |

Tue Feb 14: 10-12, B2-060 | Lecture 34: Review. Cramer's rule. Problems. | [EMEA] 13.8 | Problem set 34 |

Thu Feb 16: 10-12, B2-060 | Lecture 35: Inverse matrices and determinants. | [EMEA] 13.6 - 13.7 | Problem set 35: Thu 12-14, B2-085 |

Tue Feb 21: 10-12, B2-060 | Lecture 36: Review. Problems. | Problem set 36 | |

Thu Feb 23: 10-12, B2-060 | Lecture 37: Applications. Computing with matrices and vectors. | [EMEA] 12. 6 - 12.7 | Problem set 37: Thu 12-14, B2-080 |

Tue Feb 28: 10-12, B2-060 | Lecture 38: Functions in two variables. Partial derivation. | [EMEA] 14.1 - 14.3 | Problem set 38 |

Thu Mar 02: 10-12, B2-060 | Lecture 39: Hessian matrices. Gradientens. Tangents of a level curve. | [EMEA] 14.6, 15.3 | Problem set 39: Thu 12-14, B2-085 |

Tue Mar 07: 10-12, B2-060 | Lecture 40: Review. Linear approximations. | [EMEA] 15.8 | Problem set 40 |

Thu Mar 09: 10-12, B2-060 | Lecture 41: Stationary points. The second derivative test. | [EMEA] 17.1 - 17.3 | Problem set 41: Thu 12-14, B2-080 |

Mar 03 - 10 | Course paper EBA11801 (resit) | ||

Mar 13 - 20 | Course paper EBA11803 | ||

Tue Mar 21: 10-12, B2-060 | Lecture 42: Problems from the course paper. | Problem set 42 | |

Thu Mar 23: 10-12, B2-060 | Lecture 43: Global max/min. Extreme value theorem. | [EMEA] 17.5 | Problem set 43: Thu 12-14, B2-080 |

Tue Mar 28: 10-12, B2-060 | Lecture 44: Review. Optimization with constraints. | [EMEA] 7.6 | Problem set 44 |

Thu Mar 30: 10-12, B2-060 | Lecture 45: Method of Lagrange multipliers. | [EMEA] 18.1 | Problem set 45: Thu 12-14, B2-080 |

Thu Apr 13: 10-12, B2-060 | Lecture 46: Examples. Explanation of Lagrange's method. | [EMEA] 18.3 - 18.4 | Problem set 46: Thu 12-14, B2-080 |

Thu Apr 20: 10-12, B2-060 | Lecture 47: Interpretation of Lagrange multipliers. | [EMEA] 18.2 | Problem set 47: Thu 12-14, B2-080 |

Thu Apr 27: 10-12, B2-060 | Lecture 48: Review. Problems. | Problem set 48: Thu 12-14, B2-080 | |

Fri May 05: 09-12 | Midterm exam EBA11802(resit) | All material from the autumn semester. | |

Wed May 24: 09-14 | Final exam EBA11804 | All material from the autumn and spring semester. | |

Autumn semester | Lecturer Runar Ile (Office B4-023); Office hours Tue 12-14 (by appointment) | Reading | Problems |

Wed Aug 24: 10-12, B2-060 | Lecture 1: Basic algebra. | [EMEA] 2.1 - 2.5, 2.7 | Problem set 1: Wednesday 12-15, B2-065 |

Tue Aug 30: 10-12, B2-060 | Lecture 2: Rates of change. Powers and roots. Interest. | [EMEA] 2.2, 11.1, 11.3 | Problem set 2 |

Wed Aug 31: 10-12, B2-060 | Lecture 3: Present value of cash flows. Internal rate of return. | [EMEA] 11.5.1 - 11.5.4 | Problem set 3: Wednesday 12-15, B2-065 |

Tue Sep 06: 10-12, B2-060 | 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 07: 10-12, B2-060 | 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 12-15, B2-065 |

Tue Sep 13: 10-12, B2-060 | Lecture 6: Review. Linear and quadratic equations. | [EMEA] 3.1, 3.3 | Problem set 6 |

Wed Sep 14: 10-12, B2-060 | Lecture 7: Equations with parameters. Polynomial equations. | [EMEA] 3.2, 4.7 | Problem set 7: Wednesday 12-15, B2-065 |

Tue Sep 20: 10-12, B2-060 | Lecture 8: Review. Polynomial division. Factorization. | [EMEA] 4.7 | Problem set 8 |

Wed Sep 21: 10-12, B2-060 | Lecture 9: Rational and radical equations. Inequalities. | [EMEA] 3.4 - 3.5, 2.6 | Problem set 9: Wednesday 12-15, B2-065 |

Wed Sep 28: 10-12, B2-060 | Lecture 10: Functions and graphs. Linear and quadratic functions. Revenue and cost functions. | [EMEA] 4.1 - 4.6 | Problem set 10: Wednesday 12-15, B2-065 |

Tue Oct 04: 10-12, B2-060 | Lecture 11: Review. Some problems from Problem set 10. | ||

Wed Oct 05: 10-12, B2-060 | Lecture 12: Circles and Ellipses. Polynomial functions. Rational functions and asymptotes. | [EMEA] 6.3.1 - 6.3.3, 5.4 - 5.5, 4.7, 7.9 | Problem set 12: Wednesday 12-15, B2-065 |

Tue Oct 11: 10-12, B2-060 | Lecture 13: Review. Continuity and intermediate value theorem. Inverse functions. | [EMEA] 7.8, 7.10, 5.2 - 5.3 | Problem set 13 |

Wed Oct 12: 10-12, B2-060 | Lecture 14: Exponential functions and logarithms. | [EMEA] 4.9 - 4.10 | Problem set 14: Wednesday 12-15, B2-065 |

Oct 14 - 21 | Course paper EBA11801 - Solutions | Course paper: Wednesday 12-15, B2-065 | |

Tue Oct 25: 10-12, B2-060 | Lecture 15: Some problems from the Course paper | Problem set 15 | |

Wed Oct 26: 10-12, B2-060 | 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 12-15, B2-065 |

Tue Nov 01: 10-12, B2-060 | Lecture 17: Review. Stationary points and extreme points. | [EMEA] 9.1 - 9.2, 6.3 | Problem set 17 |

Wed Nov 02: 10-12, B2-060 | Lecture 18: Optimization in one variable. | [EMEA] 9.4, 9.6 | Problem set 18: Wednesday 12-15, B2-065 |

Tue Nov 08: 10-12, B2-060 | Lecture 19: Review. Implicit differentiation. | [EMEA] 7.1 | Problem set 19 |

Wed Nov 09: 10-12, B2-060 | Lecture 20: Second order derivatives. Convex and concave functions. | [EMEA] 6.9, 9.6, 8.5 - 8.6 | Problem set 20: Wednesday 12-15, B2-065 |

Nov 07 - 14 | Course paper EBA29103 (retake) | ||

Tue Nov 15: 10-12, B2-060 | Lecture 21: Review. L'Hôspital's rule. | [EMEA] 7.12 | Problem set 21 |

Wed Nov 16: 10-12, B2-060 | Lecture 22: Marginal cost and revenue. Average unit cost. Cost optimum. | [EMEA] 6.4, 9.3, 9.5 | Problem set 22: Wednesday 12-15, B2-085 |

Tue Nov 22: 10-12, B2-060 | Lecture 23: Review. Elasticity. | [EMEA] 7.7 | Problem set 23 |

Wed Nov 23: 10-12, B2-060 | Lecture 24: Linearisation. Taylor polynomials. | [EMEA] 7.4 - 7.5 | Problem set 24: Wednesday 12-15, B2-065 |

Thu Dec 08: 14-17 | Midterm exam EBA11802 - Solutions | ||

Mon Dec 19: 09-14 | Final exam EBA29104 - Solutions (retake) | ||