Module Directory

The module covers the mathematical skills needed to proceed to any degree course where knowledge of mathematics to A-level standard is required. The syllabus initially covers some basic mathematics of number work, Equations and Curve Sketching to ensure that all students have acquired basic skills before proceeding on to more advanced topics.

The syllabus then expands to cover Trigonometry, Calculus, Further Algebra and Series, with lectures developing in range and content. The associated work in classes will help students develop Mathematical problem-solving skills and apply them to problems in other relevant subject areas such as economics, financial maths and engineering.

The aims of this module are:

• To provide students from a wide range of educational backgrounds with a broad understanding of basic and essential mathematical skills.


• To demonstrate how Essential Mathematics knowledge can be applied in various practical applications, e.g., economics, finance and engineering contexts.


• To give students the opportunity to engage actively with activities and class worksheets provided during lectures and classes.


• To develop the ability to acquire knowledge and skills from lectures, textbooks and class work exercises, and from the application of theory to a range of problems.


• To enable students to develop their problem-solving skills by using relevant and appropriate mathematical techniques.

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

1. Use and understand basic arithmetic and algebra in problem-solving.


2. Solve linear single and simultaneous equations; linear inequality and regions; quadratic equations; functions.


3. Sketch linear and quadratic curves; formulas; rules of logarithm.


4. Understand and use differentiation; gradients of curves; equations of tangent and normal.


5. Solve and sketch cubic, log, exponential and trigonometric equations, functions and trigonometric identities.


6. Understand and use Integration; rules of integration; area under the curve.


7. Understand sequences and series; arithmetic and geometric series; solve and sketch Modulus equations and functions.

Skills for your professional life (Transferable Skills)

By the end of this module, students will have practised the following transferable skills:

1. Advanced numerical skills: this is extremely useful in any areas of Mathematics, Engineering, or in less Mathematical subjects such as Economics, etc.


2. b) Algebra: essential in all areas where Mathematics is an inherent part, such as Mechanics, Electronics, and similar subjects. Algebra is the core skill in all numerical fields of study and work.


3. Calculus: is the crown of advanced Mathematics in Mathematical sciences, as well as Applied Mathematical fields such as Electronics, modelling such as climate modelling, and of course pure Mathematics if you intend to pursue your studies in this area.


4. Visualization and Graphs: extremely important skills in both pure and applied Mathematical subjects such as Electronic Engineering, Mechanics and indeed in all quantitative fields of studies and professional practice.


5. IT skills: by practising on the NUMBAS platform and using open-source tools such as Geogebra, you will learn how to use technology to enhance your learning and increase your efficiency and productivity in your workplace.


6. Logical approach: doing advanced topics in Mathematics helps you develop additional skills in planning, analysing, and learning methodical and logical approaches to problem-solving. These skills are transferrable to many areas of your future studies and work.

Syllabus

• Essential arithmetic and number work.


• Algebra: algebraic expressions; solution of linear, simultaneous, quadratic and cubic equations; logarithms; inequalities; trigonometric ratios and functions for any angle.


• Graphical representation of functions and inequalities; curve sketching; graphical solution of equations; Tangents and Normals.


• Calculus: differentiation and integration of linear, trigonometric, logarithmic and exponential functions, including the function of a function, products and quotients; second derivative; turning points; applications of differentiation; methods of integration; definite integration; areas under curves.


• Trigonometry and trigonometric identities.


• Sequences and series: arithmetic and geometric progressions; summation and convergence of a series; binomial theorem.

This module will be delivered via:

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

Teaching and learning on Essex Pathways modules offers 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.

All lecture notes, classwork exercises and Lab exercises are placed on Moodle prior to the teaching events for easy student access. Lecture notes will be supported by audio input for each lecture slide to make it easier to follow the topics on the slide. Students are expected to complete the lab exercises in labs and/or in their own individual study time. Support for this is provided via email and through academic support hours.