Module Directory

This module covers the mathematical and statistical skills needed to proceed to any degree course within the School of Life Sciences. The syllabus covers the mathematics of basic arithmetic and algebra, graphs and rates of change as well as statistical distributions and hypothesis testing.

The associated work in classes and lab sessions develops the skills used to solve problems applicable to the study of Life Sciences, with classwork and online assignments being set and full solutions provided as part of the feedback process.

The aims of this module are:

• To ensure that students from a wide range of educational backgrounds have an understanding of core mathematical skills needed within the study of Biology and Chemistry.


• To develop the ability to acquire knowledge and skills from lectures, classwork exercises, and mathematical software and application of theory to a range of weekly tasks including data sets/examples that have a biological or chemical theme.


• To develop students' ability to use these skills in their subsequent degree courses.


• To equip students with the mathematical techniques needed to solve problems involving units, molarity and concentrations and to clearly structure their solutions and conclusions.


• To develop students’ ability to plot different types of graphs, including the use of functions and analyses of rates of change through simple differentiation.


• To give students the ability to present and interpret data relevant to their degree clearly and unambiguously, both by hand and with the use of Excel software.


• To give students an understanding and ability to calculate statistical measures and set up hypothesis tests.

By the end of this module, students will be expected to be able to:

1. Understand and use basic arithmetic and algebra.


2. Ability to plot basic graphs and find key points on graphs.


3. Understand and use differentiation to find the gradient of functions and interpret the rate of change.


4. Ability to convert between units and compute molarity and concentration calculations.


5. Understand basic statistics and calculate measures of centrality and spread.


6. Understand the differences between qualitative and quantitative data and how to choose the right chart or graph for a given data.


7. Understand and interpret basic statistical graphs.


8. Ability to calculate the centrality and spread from frequency distribution tables.


9. Understand basic concepts of probability.


10. Understand the normal distribution and be familiar with reading statistical tables.


11. Understand basic statistical inference and be able to construct simple hypothesis tests.

Skills for your professional life (Transferable Skills)

By the end of this module, you will have practised the following transferrable skills:

1. Analytical Skills. Mathematics will enhance your ability to:
- Think clearly.
- Pay attention to detail.
- Manipulate precise and intricate ideas.
- Follow complex reasoning.
- Construct logical arguments and expose illogical ones.

2. Problem-solving Skills. You will be given countless mathematical problems to solve. Experience with these will teach you to:
- Formulate a problem in precise terms, identifying the key issues.
- Present a solution clearly, making your assumptions explicit.
- Gain insight into a difficult problem by looking at special cases or sub-problems.
- Be flexible and approach the same problem from different points of view.
- Tackle a problem with confidence, even when the solution is not obvious.
- Seek help when you need it.

3. Investigative Skills. During the course of the module, you will sometimes find yourself trying to understand mathematics that seems too hard, and trying to solve problems that at first seem impossible. You should find yourself:
- Looking up lecture notes, textbooks and reference books.
- Scouring the library.
- Extracting information from every mathematician you meet (other undergraduates, postgraduates, tutors and lecturers).
- Thinking

4. Communication Skills. You will develop a capacity to assimilate and communicate highly technical information. During lectures, you will be required to organise and record a mass of mathematical detail, both spoken and written. Classroom and lab exercises will call for clear mathematical exposition. Through these experiences you will have the opportunity to learn how to:
- Listen effectively.
- Write mathematics well.
- Write essays and reports.

5. IT Skills. You will have access to computing facilities. You will have the opportunity to:
- Learn the syntax of Mathematics.
- Solve problems using mathematical software (Numbas/Excel).

6. Good Working Habits. To be a successful mathematics student you will have to:
- Be thorough and painstaking in your work.
- Organise your time and meet deadlines.
- Work under pressure, especially near exam time.
- Work independently, without constant support from teachers.
- Work cooperatively with others to solve common problems.

7. Sustainability. Green issues are embedded in the curriculum to help you develop an ethical view of the world and enhance your ability to:
- Take social responsibility.
- Understand environmental issues and prepare for the green jobs of the future.

Syllabus

• Basic arithmetic and algebra.


• Unit conversions and concentration calculations: conversions between %, concentrations, moles, and molar solutions.


• State of compounds, weight per volume for solids in solution and volume per volume.


• Conversion of units from standard SI and non-SI units in physiological ranges including grams up to kilograms or larger (for ecological scenarios) or down through, micro -, nano- (grams/moles).


• Logarithms.


• Graphical representation of functions.


• Introductory Calculus: basic differentiation of linear and polynomial functions.Descriptive statistics: Interpreting data, measures of location and dispersion.


• Inference Statistics: basic hypothesis testing, normal distribution and statistics tables.


• Using Excel to carry out statistical computations and create graphs.


• Practical application of algebra and statistics to life sciences-related problems.


• Ability to use time series graphs to visualise trends in counts or numerical values over time.


• Ability to use scatter diagrams to identify the correlation of two variables.


• Descriptive statistics: interpreting data, measures of location and dispersion.


• Key probability concepts.


• The normal distribution, reading statistical tables.


• Inference Statistics: basic hypothesis testing, the z-test.


• Using Excel to learn key formulas, find summary statistics, carry out statistical computations and create graphs.


• Ability to propose an appropriate sampling method for a given scenario and understand its limitation.


• Define the terms sampling unit, sample, population, statistic and parameter and explain the relation between them.


• Define and explain the meaning of the following terms; null hypothesis, alternative hypothesis, test statistic, sampling distribution, significance level, rejection region, critical value, and decision rule.


• Explain the meaning of one-tailed and two-tailed hypothesis tests.


• Interpret and use tables of critical values.


• Use basic functions in Excel to analyse and produce graphs.

This module will be delivered via:

• One 1-hour lecture per week.
• One 2-hour class per week.
• One 1-hour lab session per week.

There are two weeks of revision lectures and classes in the Summer Term. The first 10 weeks of the Autumn Term focus on Mathematics, with the subsequent 10 weeks of the Spring Term focusing on Statistics.

All lecture notes and worksheets are accessible via Moodle. Listen Again is also used as part of learning support in which students can review the recordings at a later date.

Teaching and learning on Essex Pathways modules offer students the ability to develop the foundation knowledge, skills, and competencies to study at the undergraduate level, through a curriculum that is purposely designed to provide an exceptional learning experience.

All teaching, learning and assessment materials will be available via Moodle in a consistent and user-friendly manner.