Math skills preparation

In the first semester, the course Mathematics for Statisticians will level up the necessary mathematical knowledge for successfully completing the master program. The minimum entry level for this course is equivalent to Dutch high school VWO Mathematics A. Detailed information, instruction video’s and excersises to get your math skills (back) in shape quickly, can be found here.

You can find a specification of the minimum entry requirements, corresponding with the Dutch VWO Wiskunde A level here.

For preparation, you can use the book that is also used for the course “Mathematics for Statisticians” in the first semester.

Calculus a complete course, Robert A. Adams &Christopher Essex, 2013 Pearson Education Canada ISBN-13 978-0-321-78107-9

Below we give an overview of the paragraphs from the book you are required to know by the beginning of the course (and thus the master), with links to video’s from our own teachers and from the Khan Academy. In this way you can revise the content and all students are on the same page when they arrive at the first lecture. This material will be examinated in the first week(s) of the course Mathematics for Statisticians.

The material looks like a lot, but there is overlap between the different video’s, and you should have learned most, if not all, in high school. Since high school might be some time ago for you, and many of you have not brought your math skills in practice since, we provide the material below to get you back in shape quickly! We advise you to start with reading the book’s paragraphs, and then watch the videos that correspond to the parts you find difficult. We also made a self test, for which you can learn all necessary skills from the book and the video’s below. If you have no problems with the self test, you are completely prepared for the master!

The answers to the self test can be found here:
Exercises 1-4
Exercises 5-8
Exercises 9-10
Exercises 11-13
Exercises 14-16

 

Study material

Functions and graphs
Book paragraphs:    P.3, P.4, P.5, P.6, P.7, 1.2, 1.4, 3.2, 3.3

Video lectures: 

Functions 1
Functions 2
Domain and Range (KA)
Composing functions (KA)
Piecewise functions (KA)

Exponential Functions 1
Exponential Functions 2
Logarithms
Exponential growth and decay (KA)

Logarithms (KA)
Logarithmic equations (KA)

Linear Equations
Quadratic Equations 1
Quadratic Equations 2
Quadratic Equations 3
Polynomials 1
Polynomials 2

Factoring Quadratic functions (KA)
Solving Quadratic equations (KA)

Trigonometry 1
Trigonometry 2

You can work on the following exercises to get some routine with these type of problems.

P.3: 1-20, 35-40,43-46,
P.4: 1-8, 23-38,
P.5: 1, 2, 8, 9, 11-16, 19-24,
P.6: 1-4,
P.7: 1-18,
3.2: 1-18, 25-30,
3.3: 1-14.

Differentiation

Next, we focus on differentiation. We introduce the notion of a derivative, and learn how to compute derivatives of standard functions. Also, we will use the quotient-, product- and chain rules to compute derivatives of more complex functions. 

Book: 2.1, 2.2, 2.3, 2.4, 2.5

Video Lectures:

Differentiation
Derivatives (KA)
Derivatives and graphs (KA)

Differentiation Applications 1
Standard Derivatives
Power Rule (KA)
Product Rule and Quotient Rule
Product Rule and Quotient Rule (KA)

Chain Rule 1
Chain Rule 2
Chain Rule (KA)

Exercises to practice with (this is a lot, choose wisely which exercises you choose to do!)

2.1: 1-12, 18-21
2.2: 30-49
2.3: 1-41, 43-47
2.4: 1-8, 11-16, 22-34
2.5: 3-5, 8-17, 19-22, 25-32, 35-38, 45

Extreme values

Book paragraphs: 4.4, 4.8

Video Lectures:

Extreme values 1
Extreme values 2
Extreme values 3

Critical values and graphing (KA)
Extreme values (KA)
Optimization (KA)

Exercises:

4.4:    1-6, 10-39.
4.8:    1-4, 7-9, 17,18.

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