Last updated March 2023

### Contents

- Algebra
- Differentiation
- Differentiation: maxima and minima
- Fractions and Percentages
- Functions and Graphs
- Geometric progressions: interest and growth
- Integration
- Linear Equations
- Linear Programming
- Logarithms and Indices
- Matrices
- Probability and Expectation
- Sigma notation
- Simultaneous (linear) equations
- Other links to resources

### Algebra

- Handouts from Mathtutor
- Refresher booklet, videos and self-tests from Mathtutor
- Formative assessments can be selected from the
*maths e.g.*Numbers and Algebra topics especially:

### Differentiation

- Teaching and Learning guide from METAL
- Powerpoint slides from METAL
- Handouts from Mathtutor
- Self-test materials from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Differentiation and Economics topics especially:

### Differentiation: maxima and minima

- Video, exercises and 10 page booklet from Mathtutor
- Leaflets and handout from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Differentiation and Economics topics especially: - Join our Question Bank for problem sets on this topic
### Fractions and Percentages

- Films and animations from METAL
- Explanatory text and examples from Math You Need Econ
- Video clips, text and self-tests from Mathcentre
- Marginal Analysis: text and examples from Math You Need Econ
- Handouts on fractions, ratios, percentages and roots from Mathtutor
- Formative assessments can be selected from
*maths e.g.*especially: - Case study: "Measuring inequality: Using the Lorenz Curve and Gini Coefficient"
- Case study: "Economic Growth: What Factors Matter?"
- Join our Question Bank for problem sets on this topic

### Functions and Graphs

- Functions and Inverses: video and quizzes from Refresher Mathematics for Economics
- Review of Graphs: Visual Display of Information from Syracuse University
- Understanding Graphs: text and self-test problems from Math You Need Econ
- Graphing Data: text and self-test problems from Math You Need Econ
- Handouts from Mathtutor
- Video clips, text and self-tests from Mathcentre
- Teaching and Learning Guide on Non-linear equations from METAL
- Formative assessments can be selected from the
*maths e.g.*Algebra and Elementary Functions topics especially:

### Geometric progressions: interest and growth

- Sequences and Series: video and quizzes from Refresher Mathematics for Economics
- Teaching and Learning guide: Finance and Growth from METAL
- Films and animations from METAL
- Videos and other materials on series from Mathtutor
- Video clips, text and self-tests from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Algebra and Economics topics especially: - Case study: "Affording the mortgage" (geometric progression)
- Case study: "Does income constrain household spending?"
- Case study: "UK house prices: Going through the roof?"
- Case study: "Spending on plastic: the potential for financial distress"
- Case study: "Saving for the Future: Don't leave it too late!"
- Case study: "Economic Growth: What Factors Matter?"

### Integration

- Video and quizzes from Refresher Mathematics for Economics
- Teaching and Learning guide from METAL
- Introduction to Integration from MathsIsFun.com
- Handouts from Mathtutor
- Text and self-tests from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Integration topic especially: - Case study: "Estimating a demand curve for un-priced environmental goods" (example of using a definite integral)
- Case study: "Affording the mortgage" (definite integral)
- Case study: "Saving for the Future: Don't leave it too late!"

### Linear Equations

- Teaching and Learning guide from METAL
- Slope: Explanatory text and examples from Math You Need Econ
- Linear Equations from MathsIsFun.com
- Films and animations from METAL
- Video, text and self-tests from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Coordinate geometry topic especially: - Case study: "Household spending: When income matters in the end"

### Linear Programming

- Teaching and Learning Guide on Linear Programming from METAL
- Teaching and Learning Guide on Partial Differentiation from METAL
- Formative assessments can be selected from the
*maths e.g.*Linear Programming topic especially:

### Logarithms and Indices

- Videos and quizzes from Refresher Mathematics for Economics
- Two-page handout on indicial equations from Mathcentre
- Introduction to logarithms from MathsIsFun.com
- Video, handouts and self-tests in exponential & logarithmic functions from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Algebra and Elementary Functions topics especially: - Case study: "Do households smooth their consumption?"
- Case study: "Deriving constant price estimates of GDP: An illustration of chain-linking"
- Case study: "UK house prices: Going through the roof?"
- Case study: "Economic Growth: What Factors Matter?"

### Matrices

- Videos and quizzes from Refresher Mathematics for Economics
- Teaching and Learning Guide from METAL
- Handouts and video from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Matrices and Economics topics especially: - Introduction to Matrices from MathsIsFun.com
- Essence of Linear Algebra (YouTube playlist) 3Blue1Brown

### Probability and Expectation

- Probability from MathsIsFun.com
- Formative assessments can be selected from the
*maths e.g.*Probability topic especially: - Case study: "Counting the cost of effective health policy" (probability in sensitivity analysis)
- Case study: "Probability in action: Gambling, the US Presidency and the market for car insurance" (betting odds and conditional probabilities)

### Sigma notation

- Introduction to Sigma Notation from MathsIsFun.com
- Sums, series and Sigma summation notation: video and quizzes from Refresher Mathematics for Economics
- Video, handout and self-tests from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Algebra and Economics topics especially: - Case study: "Measuring the competitiveness of sport: are the top teams getting too strong?" (Concentration ratio)
- Case study: "Is the Scottish Premier League less competitive than its English Counterpart?" (Hirschman-Herfindahl Index)
- Case study: "Measuring health improvements for a cost effectiveness analysis"

### Simultaneous (linear) equations

- Systems of linear equations: video and quizzes from Refresher Mathematics for Economics
- Teaching and Learning guide from METAL
- Films and animations from METAL
- Explanatory text and practice problems from Math You Need Econ
- Video and animations from Mathtutor
- Video, text and self-tests from Mathcentre
- Formative assessments can be selected from the
*maths e.g.*Algebra and Economics topics especially:

Our printable Maths Formula Sheet has helpful reminders for most of the above topics

Interactive Economics Facts and Formulae is a 12-page document by Martin Greenhow (Brunel University) with quick summaries for many applications of maths in economics, and copious links to questions in the Maths E.G. database.

### Other links to resources

#### Teaching and learning materials

#### Latest Addition

George Orlov and Doug McKee, Cornell UniversityA freely usable library of standardised assessments for economics students, with an option to deliver the assessments online and have a summary report emailed to the lecturer. These are designed as "an objective, repeatable measure of what your students know about a particular subject" and so support testing of prerequisites for a course and enable pedagogical research.

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