# Essential Maths and Stats for Higher Education

##### Description

**Essential Maths and Stats** provides a comprehensive overview of tertiary level mathematics and statistics and is the only definitive New Zealand text for mathematics and statistics at entry level. It is also an excellent ‘extension’ text for secondary school students.

Divided into six key sections Numerical Mathematics, Algebra (1 and 2), Trigonometry, Calculus and Statistics the text includes: differential equations, integration techniques, networks, differential equations, vectors, determinants, matrices, linear programming, probability distributions, hypothesis testing, correlation, regression, chi-squared tests and ANOVA.

The text provides full explanations, worked examples and a wide variety of graded exercises (with solutions) and is structured so that readers can dip in and out and refer to relevant sections on a need-to-know basis.

**Click ****here**** to view sample pages online** (3.3MB)

**Additional Resources**

**For Students:** Users of the textbook also have access to online digital resources and supplementary content including: Links; Spreadsheets; Supplementary exercises. Click on the Student Downloads tab to view and download files.

**For Lecturers: MyMathLab Global** is a powerful online homework, revision and assessment tool to help students and instructors. MyMathLab Global engages students in active learning – it is modular, self-paced, accessible anywhere with internet access and adaptable to each student’s learning style. Contact your Pearson Education Consultant to find out more.

##### Table of contents

Introduction

Other resources

About the authors

**Section 1: Numerical mathematics
** 1 The basics: integers, decimals, fractions, percentages

2 Order of operations, powers, roots

3 The metric system, area, volume, speed, density, flow

4 Standard form, approximation

5 Rates, ratios, proportion

6 Indices, logarithms, index equations

7 Financial mathematics

8 Spreadsheets

**Section 2: Algebra 1
** 9 Basic algebra 1: expansions, solving linear equations and inequations,algebraic fractions

10 Basic algebra 2: factorising, rearranging formulae, simultaneous equations, quadratic equations

11 The quadratic formula, completing the square, nature of roots

12 Graphs 1: straight lines, parabolas, cubics

13 Graphs 2: functions and transformations

14 Graphs 3: hyperbolas, circles, exponential graphs, logarithmic graphs

**Section 3: Trigonometry
**15 Right-angled triangles: Pythagoras, trigonometric ratios, bearings,trigonometry in three dimensions, special triangles

16 Sine and cosine rules, radians, arcs, segments

17 Trig graphs and equations

**Section 4: Calculus
**18 Limits, continuity, gradients, derived functions, first principles, differentiability

19 Differentiation rules, differentiation of composite functions products and quotients, l’Hopital’s rule

20 Applications of differentiation: tangents, stationary points,rates of change

21 Differentiation of parametric functions, implicit differentiation

22 Integration of polynomials, definite integration, areas

23 Integration of other functions, integration by substitution

24 Calculus applications: kinematics, solids of revolution

25 Differential equations

26 Integration by parts, partial fractions, integrating factors

**Section 5: Algebra 2
**27 Networks

28 Arithmetic and geometric sequences

29 Infinite series

30 Long division, remainder and factor theorems

31 Vectors, determinants, matrices

32 Linear programming

**Section 6: Statistics
**33 Averages, data display, sampling methods, standard deviation

34 Probability

35 Expectation algebra, linear combination of random variables

36 Factorials, permutations, combinations

37 Binomial theorem, binomial and Poisson distributions

38 Normal distribution, distribution of the sample mean and total, linear combinations

39 Hypothesis testing, confidence intervals, t-distribution

40 Correlation and regression

41 Chi-squared tests, ANOVA

**Appendices
**Appendix 1: Proofs

Appendix 2: Useful formulae

Appendix 3: Statistical tables

**Answers**

##### Features & benefits

**Introduction**

**Essential Maths and Stats** will be an invaluable resource for all students taking entry-level mathematics and statistics courses at New Zealand tertiary institutions. In addition, it is an ideal text to extend the abilities and understanding of secondary school students who are capable of extension work.

The scope of **Essential Maths and Stats** is from Year 10 secondary school mathematics right through to first and second year university mathematics and statistics papers. If a student is specialising in these subjects, he or she will find that this book provides a strong foundation from which to continue to degree level, either within New Zealand or internationally. If the student requires some mathematics or statistics in order to complete the requirements for a degree or diploma in another subject, or for a ‘bridging’ mathematics course, he or she will find that the essentials needed are all contained in this volume, and are explained clearly and without assumptions of prior knowledge of mathematics.

The topics at secondary level include, but are certainly not limited to, material for mathematics and statistics at NCEA (NZ) Levels 1 and 2 of the New Zealand mathematics curriculum (Years 11 and 12), as well as most of the material in both disciplines at Level 3(Year 13).

In addition, the following topics at tertiary level are included:

- Algebra: matrices and vectors; the Taylor and Maclaurin series; hyperbolic functions
- Calculus: l’Hopital’s rule; integration by parts; integration using partial fractions; integrating factors
- Statistics: t-distribution; hypothesis testing; chi-squared distribution; ANOVA.

The book is divided into six sections:

- Numerical mathematics (clarifying the ‘basics’ of mathematics and outlining the essential tools)
- Algebra 1
- Trigonometry
- Calculus
- Algebra 2
- Statistics (including probability).

Also included is a chapter on spreadsheets for those wishing to improve their computer skills.

Both secondary level and more advanced topics are presented in a clear and concisemanner, to furnish the student with a solid mathematical foundation – he or she will then understand the methods involved and derive satisfaction from that understanding.

Connections between different areas of mathematics are explained. The discussion is not overly theoretical, but rather emphasises the practical methods needed to achieve a mastery of each topic and a clear understanding of the process.

The chapters are designed so that they are essentially progressive: as far as possible one topic and one chapter lead onto the next. However, as the scope of mathematics and statistics is large, the student will very likely find him/herself jumping around the chapters, at least to a small extent, guided by the chapter headings.

David Barton

David Cox

##### Author biography

**David Barton**is one of the best known mathematics writers in New Zealand. Educated at Victoria University of Wellington, he gained a Senior Scholarship before graduating with a BA (Hons) in Mathematics and Statistics. David wrote the previous edition of this text, titled

*Maths for Higher Education*, and his texts have also been adapted for Australia, South Africa and Abu Dhabi.

**David Cox**is a mathematics and statistics tutor at tertiary and secondary levels in Christchurch, New Zealand. Since completing a BA in Maths and Music at Victoria University of Wellington he has been a sought-after teacher for a wide range of mathematical courses for over twenty years. David also plays Principal Horn with the Christchurch Symphony Orchestra.