• Professional Development
  • Medicine & Nursing
  • Arts & Crafts
  • Health & Wellbeing
  • Personal Development

97 Marketing courses in Leominster

CONSULTATIVE SELLING Training Programme Framework

By Dickson Training Ltd

Key Objectives for the Training provision Effective listening to a client's needs and requirements during various stages of the sales process. Engage in meaningful communication with clients, learn to identify challenges and opportunities that relate to the prospects. Overcome the identified challenge. Build long term rapport and establish trust with the prospect throughout the sales process, Ensure continued customer satisfaction that can turn into repeat business. Be able to build rapport with customers or clients. Know the right questions to ask to fully understand the customer or client’s needs without putting on any pressure. Be able to check you have the right information from the customer or client. Be able to match products and services to the customer or client using the information you have gathered. Be able to influence effectively. Know how to stand out from your competitors. Stage 1 – Research the Company’s ‘Value Propositions’ and USP Analysis  Conducting 30 min confidential interviews with a cross-section of the eligible Attendees & the Stakeholders, in order to gain an objective understanding of the various scenarios and clients that the Participants work with. the Company’s ‘Value Propositions’ Unique Selling Points The Customers’ journey(s) The Competition’s offers for analysis and comparisons. From these findings, a carefully calibrated bespoke Programme will be designed and delivered.  Stage 2 - Design the Bespoke 2 x day Course  nd Stage 3 - Delivery of the Course Programme This Programme can be delivered in 2 x consecutive days, or split between 2 – 3 weeks, to make it more ‘work-friendly’ – if required. It is very practical and commercially focussed in approach, with lots of interactive exercises designed to draw out the learning applications via the debriefings. The ‘Real Play’ scenarios on day 2 will be based on specific case studies drawn from the Research findings so that they are authentic to optimise the learning. Individual Action Plans will be captured at the end of each day to be debriefed by the Participants’ respective Line Managers.  Template Programme Day One – Foundation – Strategic Approach Section One – The Principles of Consultative Selling Defining ‘Consultative Selling’ The Company’s ‘Unique Selling Points’ & Value Proposition The Consultative Selling model – the five stages Avoiding appearing ‘pushy’, ‘pressurising’ or ‘talking through the sale’ Section Two –Strategy & Preparation  ‘Buy-Class’ Matrix Strategic plan Template – matching services/products to identified needs & opportunities. Preparing a range of objectives Constants and variables – USP’s Researching key Client/Decision Makers’ priorities, profile & background (LinkedIn etc.) Preparing for potential & likely Objections Section Three – Email etiquette & ‘influencing’ email correspondence.  Email etiquette A.B.S.U.R.D model Clarity and tone – discovery of clients’ needs & motivational factors. Techniques to influence and ‘nudge’. Ensuring the data and content have a ‘gentle’ motivational & appealing message. Top Tips Day Two – Practical Application Section Four – Rapport Building & Effective Communication skills ‘Behaviour Labelling’ techniques – setting a positive tone. Asking Open Questions – gaining a full understanding of the clients’ priorities & expectations. EQ - Inviting opinions; perspectives; experiences – winning confidence. Active Listening – focus and commitment to understand. ‘Reading the room’ – adapting to responses and reactions. Maintaining focus on relevant topics that the Client cares about; carefully consider the opportunities to influence. But NO PRESSURE! Building a ‘bond of trust’ with commitments and authentic, shared values. Section Five – Explaining the Benefits – aligned to the Customers’ Priorities Understanding ‘Why do People Buy?’ Research data analysis. Open questions that lead to understanding the key issues and Clients’ priorities. Avoiding the danger of ‘pressurising’ the Client. Responding to objections effectively, with confidence and sensitivity. Explaining the benefits that are aligned to the Clients’ stated requirements. Making the Data ‘sing’ – memorable takeaways for the Client. Augmented benefits – Brand confidence; Case studies; Warranty; Service; Range; Flexibility etc. in alignment with their stated preferences/requirements Differentials compared to Competitors Section Six – Winning Commitment Inviting commitment – with confidence Consultative Selling Closing techniques (e.g. Alternative Close/Assumptive Close et al) Avoiding ‘talking through the sale’ – knowing when to ‘Shut UP!’ Confirming agreement – ensuring Clients’ motivation for repeat business Section Seven – Practical Application ‘Real Play’ From the Research findings, carefully devised scenarios can be generated to provide the most valuable learning opportunities to underpin all the skills & techniques covered in the Programme.  Potential Real Play scenarios: A well-established customer has indicated that they are soon to be opening up additional new offices – this presents an opportunity to arrange for the Company to support them with their upcoming needs. After some very positive feedback and with the upcoming contract renewal imminent – how can the Company give the Customer more high-quality support in other areas of their business? A Competitor has been to see the client and they have prompted some concerns about ‘value for money’ & ‘quality of service’. How Real Play works… The group is split the group into 2 sub-groups, one with our Professional Actor (option available); the other with the Trainer or a willing Participant. Each group has a brief and has to instruct their Trainer/Actor/Participant on how to approach the scenario supplied. The Actor and Trainer (or willing Participant) perform the role play(s) as instructed by their respective teams; however, during the action they can be paused for further recommendations or direction. The outcome is the responsibility of the team(s) – not the performers. Debrief the full Programme Individual Action Plans - to be followed through. ‘Best Practices’ for application into the business Options for Exercises within the Programme  Sample Exercise – Red & White  There is a specific time managed agenda and itinerary, which puts the group under pressure.  The key challenge is for the sub-groups to maximise the commercial value from the task, however there is always a great danger that the individuals attempt to gain financial progress at the expense of the other group! Debriefing points: Persuasive communication and influence across barriers Gaining buy-in when others are sceptical Strategic planning accounting for others’ behaviours Sample Exercise – Communication Challenge Each Participant has different pieces of information, but are not allowed to share it visually. They are only allowed to communicate to work out the solution hidden among the large amount of data. Debrief: Structured approach Maintaining focus through distractions/interference Active Listening Controlled communication Sample Exercise – Persuasive emails Sample emails are shared to be critiqued and improved upon to be debriefed: Tone & impact Making the Data ‘sing’ Influential & motivational language Customer centric message. Sample Exercise –Juggling   Each Participant has to pass the ‘Customers’ (Juggling balls) carefully through the system with all the other Participants to reach a profitable conclusion  Debrief: EQ to read the room and effectively communicate, when the pressure is on Customer focus and adapting to challenges Devising a plan that wins buy-in Overcoming competing ideas to get to ‘best practice’ Consistent commitment, communication and motivational drivers that influenced performance. Sample Exercise –Critical Path  The group are provided with 30 x discs and some ‘post-it’ notes. (no pens or pencils are allowed) Their brief is to create a grid shape with the 30 x discs, which will act as ‘stepping stones’ for the ‘Critical Path’ But they have to follow the correct order through the grid from the start to finish, which they will have to work out through ‘trial & error’ All of the team must pass through the ‘Critical Path’ worked out on the grid, observing the constraints, within the time limit. No talking is permitted once they start using the materials Debrief: - Clear communication focussing on the ‘client’s journey’ Planning for challenges Identifying risks and mitigating them Role allocations & support Quality control and disciplines  Sample Exercise –Back to Back  Each Participant is positioned back-to-back with a partner. They have to work out precisely what the ‘statement’ given to the other person is without looking around. Each person has a different brief. Debrief: - Asking Open Questions Active Listening Accuracy in identifying the objective.

CONSULTATIVE SELLING Training Programme Framework
Delivered in Bardsey + 3 more or UK Wide or OnlineFlexible Dates
Price on Enquiry

Customer Experience Excellence

4.9(9)

By Sterling Training

Customer service just isn’t enough. Customer experience is where the secret to success lies. Build a loyal and fruitful customer base by learning how to design frictionless processes and build empathetic and solution-focused services with our bespoke courses, which include: Customer service vs customer experience The changing nature of customers and how to stay ahead Customer needs vs customer expectations How our behaviour affects those around us and how to use the power of influence Communicating with customers positively and effectively Moments that matter Building trust and integrity What to do when things go wrong

Customer Experience Excellence
Delivered in Southampton or UK Wide or OnlineFlexible Dates
Price on Enquiry

Customer Excellence Training

By Beyond Theory: business training & coaching

leadership management training course customer service training

Customer Excellence Training
Delivered in Northampton or UK Wide or OnlineFlexible Dates
Price on Enquiry

We will help you to find the right course for you

By EU Network

Foundation Year, Bachelors degree, Masters, no IELTS needed, Student finance support

We will help you to find the right course for you
Delivered In-Person in London + 1 more or UK WideFlexible Dates
FREE

Commercial awareness in the public sector (In-House)

By The In House Training Company

The need for key staff to have commercial skills is paramount, as the public sector is increasingly opened up as a commercial market, in which organisations compete against each other and the private sector for contracts. Generating additional income and being commercially aware is vital for this to be a success, and is what many public sector organisations are looking to do. This programme will help you: See commercial awareness as not just another skill-set, but as a different mind-set Use a variety of tried-and-tested commercial, analytical decision-making techniques and tools Define your commercial objectives Develop a strategic focus Start looking at service clients as market segments Analyse, in a competitive context, your service offering Plan a commercial strategy, prepare for its implementation and see it through to execution 1 What is commercial thinking? Understand what it means to be a commercial thinker Identifying commercial opportunities often involves not only a different skill set but also a different mindset; looking at the services that you provide 2 Defining strategic commercial objectives Defining your key commercial objectives Prioritising your strategic objectives Two key strategic planning tools:Resource and Competency MatrixPESTLE How to apply these tools to your particular situation 3 Developing a strategic focus Decision-making on how to compete in the markets identified by your strategic objectives requires a strategic focus Developing strategic focus A tool for helping you to make those decisions: using the Ansoff Matrix 4 Defining customer targets How to think more commercially by understanding who all your customers are and how they differ from each other how to apply the principles to your areas to identify the type of customers you have and their key characteristics - Customer segmentation Who are your customers? How do their needs vary? - Scenarios 5 The competitive market place Understanding the competitive forces at play Different types of competition Analysing your competitive environment using Porter's 5 Forces model 6 Meeting stakeholder expectations Two simple models to help you identify the key stakeholders who could influence your commercial environment How to use your stakeholders to help you achieve your commercial objectives 7 Implementation - systems, structures and processes Effective commercial activity involves working with others to implement ideas and strategies What do you need to have in place before you implement your commercial strategy? How to health-check your organisation prior to implementation using the McKinsey 7S framework 8 Implementation - people and culture A good commercial strategy only works if the people involved buy in to the ideas and if the culture of the organisation is conducive to the effective implementation How the latest thinking in behavioural economics can help you develop your culture and people to work commercially 9 Tools and checklists Be more commercial within your sphere of influence using a commercial checklist to help you Using the checklist as a benchmark against the most commercially aware organisations Using the checklist as a health check - both corporately and individually

Commercial awareness in the public sector (In-House)
Delivered in Harpenden or UK Wide or OnlineFlexible Dates
Price on Enquiry

Introduction to sales (In-House)

By The In House Training Company

When staff are new to sales it can seem daunting, especially when they have targets to meet. If the staff you need to promote your products and services get it wrong then it can knock their confidence and negatively impact how your customers see you as an organisation. This programme provides staff with the basic skills they need to sell. This course will help participants: Profile customers Research and identify potential new customers Use the consultative sales process Build effective rapport with customers Identify customer needs through effective questioning and listening Position products and services effectively Close the sale or gain commitment to further action Manage their customer portfolio to maximise sales 1 Introduction Aims and objectives of the training Personal introductions and objectives Self-assessment of existing sales skills Overview of content 2 Knowing your customers Who are your customers, and what do they want from you? What are your strengths, compared to your competitors? Who are your new potential customers? How do you communicate with new customers? What do you need to know about your customers before you start to sell? Making the initial approach Planning your pipeline - keeping the customers coming 3 The four-step sales process Overview of the consultative sales process Key benefits of using the consultative sales process Focusing on behaviours not targets The behaviours of a good salesperson Common pitfalls and mistakes Personal strengths and weaknesses 4 Building rapport First impressions - Mehrabian theory of communication Short cuts to building rapport Looking out for clues as to how the customer is thinking Looping back to keep the conversation flowing Acknowledging past communication Dealing with emotions such as anger Setting the agenda to keep control Getting past gatekeepers 5 Questioning and listening How to ask open questions to uncover information Left brain questions When closed question can be useful What stops us listening? The four levels of listening How to develop your listening skills 6 Presenting products and services to customers When to present Using benefits not features Making it personal Using reciprocity The tendency towards the middle Using consistency 7 Gaining commitment Testing the water Dealing with objections using ACLEO Asking for the business Getting referrals Ending with a personalised close Following-up 8 Managing your customer pipeline Spotting opportunities for cross-sales Managing your portfolio Maximising sales proactively Review meetings Customer satisfaction measures and surveys Mystery shopping 9 Putting it all together Skills practice Personal learning summary and action plans

Introduction to sales (In-House)
Delivered in Harpenden or UK Wide or OnlineFlexible Dates
Price on Enquiry

Sales awareness for IT professionals (In-House)

By The In House Training Company

In the fast-changing world of business, and especially IT, everyone in the organisation should be involved in sales. One of the best ways is to give the customer an outstanding experience. The customer experience is the competitive battlefield of today. Sales may be won or lost here. You can either close a sale for a quick buck, or open a long-term relationship to create a high lifetime value customer. By developing excellent communication skills, rapport and, most of all, a desire to serve and listen to the needs of the customer to the best of their ability, both sales teams and other IT professionals will create trust, nurture relationships and develop awareness of other opportunities with the customer. By the end of this course, participants will be able to: Understand the power of a positive customer experience in developing sales opportunities Recognise and develop a sales opportunity when it arises Engage with customers and develop rapport and trust Use verbal and non-verbal communication skills and pick up on signals Ask powerful questions - and listen to the answers Create 'magic moments' for the customer Turn a complaint into an opportunity Know when to ask for referrals and testimonials Pass on leads to the relevant people 1 Introduction Aims and objectives Beliefs about sales 2 Building rapport First impressions Short cuts to rapport Finding common interests 3 Selling or serving? Managing emotions and behaviour - Transactional Analysis Moments of truth - creating 'magic moments' Speed sells - the follow-up 4 Meetings Planning a successful meeting Pre-meeting connection and assistance Sales meeting failure reasons Right v wrong mindset 5 Communication - verbal and non-verbal The 3 Vs - Visual, Verbal, Vocal Picking up on signals 7 power questions Questioning techniques LISTEN - 3 types of listening skills 6 Influencing 6 levels of influence Framing to change perspectives Turning complaints into opportunities 7 Referrals The power of referrals How and when to ask for a referral 5 steps from rapport to referral 8 Presentation and pitching (optional session) Basic presentation structure and delivery Creating powerful impressions Creating a 60-second pitch The elevator 10-second pitch - answering 'What do you do?' Sales presentations Emotion v Intellect - how to engage Using visuals

Sales awareness for IT professionals (In-House)
Delivered in Harpenden or UK Wide or OnlineFlexible Dates
Price on Enquiry

Educators matching "Marketing"

Show all 5
Black's Academy

black's academy

London

AQA A level Mathematics 7357 AS level Mathematics 7356 GCSE higher level Mathematics 8300H GCSE foundation level Mathematics 8300F Edexcel A level Mathematics 9MA0 AS level Mathematics 8MA0 GCSE higher level Mathematics 1MA1H GCSE foundation level Mathematics 1MA1F OCR A level Mathematics H240 AS level Mathematics H230 GCSE higher level Mathematics J560 GCSE foundation level Mathematics Other courses IGCSE extended level Mathematics 0580 Scholastic Apititude Test (USA Exam) GED (USA Exam) All other exams Click on any of the above links to obtain free resources Book free diagnostic now blacksacademy symbol Director Peter Fekete Educational consultancy | Curriculum design | Courses for adults | Public speaking | Publications CONTACT a CONTENT OF THE REMOTE LEARNING SYSTEM * US GRADE 6 / UK GCSE GRADE 2–3 1. Addition and subtraction 2. Starting number sequences 3. Further number sequences part I 4. Multiplication to 8 x 8 5. Further number sequences part II 6. Multiplication to 12 x 12 7. Square numbers 8. Positive and negative numbers 9. Sums 10. Shapes and perimiters 11. Measurement and areas 12. Reading information 14. Understanding fractions 15. Decimals 16. Percentages 17. Long multiplication 18. Beginning algebra 19. Beginning probability 20. Beginning geometry 21. Properties of numbers 22. Telling the time 23. Geometry in three dimensions US GRADE 7 / UK GCSE GRADE 4 1. Deeper understanding of number 2. Combinations 3. Long division 4. Operations 5. Practical problems 6. Order and type of numbers 7. Measurement 8. Time and time management 9. Fractions 10. Organising information 11. Ratio and proportion 12. Probability 13. Angles 14. Visual reasoning 15. Bearings 16. Working in two dimensions 17. Working in three dimensions 18. Transformation geometry 19. Continuing algebra US GRADE 8 / UK GCSE GRADE 5–6 1. Patterns and pattern recognition 2. Lines, regions and inequalities 3. Mastering fractions 4. Types of number 5. More about triangles 6. Measurement and computation 7. Proportionality 8. Working with space 9. Indices 10. Further work with ratio 11. Investments 12. Further algebra 13. Quadrilaterals and polygons 14. Speed and displacement 15. Continuing with probability 16. Describing data US GRADE 9 / UK GCSE GRADE 6–7 1. Further proportionality 2. Congruency 3. The tricky aspects of algebra 4. Lines and equations 5. Basic formal algebra 6. Analysis and display of data 7. Graphing functions 8. Dimension and algebra 9. Algebraic fractions 10. Circle theorems 11. Algebraic factors 12. Simultaneous equations 13. Velocity and acceleration 14. Proportionality and scatter 15. Number puzzles US GRADE 10/ UK GCSE GRADE 7–8 1. Transpositions 2. Patterns and pattern recognition 3. Algebraic manipulations 4. Quadratics 5. Surds 6. Linear inequalities 7. Functions 8. Trigonometry 9. Systems of linear equations 10. Further presentation and analysis of data 11. Polynomial functions 12. Algebraic products 13. Finding roots 14. Intersection of lines and curves 15. Indices and index equations US GRADE 11/ UK GCSE GRADE 8–9 1. Completing the square 2. Venn diagrams 3. Coordinate geometry with straight lines 4. Further trigonometry 5. Transformations of curves 6. Modulus 7. Basic vectors 8. Quadratic inequalities 9. The quadratic discriminant 10. Arcs, sectors and segments 11. Circles, curves and lines 12. Probability and Venn diagrams 13. Functions, domains and inverses 14. Trigonometric functions 15. Recurrence relations 16. Further elementary vectors FREE LEGACY RESOURCES Business Studies, Economics, History, Mathematics, Philosophy, Sociology Business Studies PEOPLE AND ORGANISATIONS 1. Management structures and organisations 2. Leadership and management styles 3. Classical theory of motivation 4. Human relations school 5. Management by objectives 6. Workforce planning 7. Recruitment 8. Payment systems MARKETING 1. The economic problem 2. Money and exchange 3. Price determination 4. Determinants of demand 5. Market analysis 6. Marketing and the product life cycle 7. Objectives and marketing EXTERNAL INFLUENCES 1. Stakeholders 2. Business ethics 3. Market conditions 4. Business and the trade cycle 5. Business and technological change 6. Business and inflation 7. Business and exchange rates 8. Business and unemployment ACCOUNTING & FINANCE 1. Cash Flow Management 2. Costs, Profits & Breakeven Analysis 3. Budgeting & Variance Analysis 4. Sources of Finance 5. Profit & Loss Account 6. The Balance Sheet 7. Depreciation by the fixed-rate method 8. Reducing Balance Method 9. Stock Evaluation 10. Working Capital and Liquidity 11. Accounting Principles and Window Dressing 12. Costing and Management Accounting 13. Investors and the Corporate Life Cycle 14. Investment Appraisal: Average Rate of Return 15. Investment Appraisal: Payback Method 16. Investment Appraisal: Net Present Value 17. Investment Appraisal: Internal Rate of Return 18. Profitability Ratios 19. Liquidity Ratios 20. Efficiency and shareholder ratios 22. Gearing and Risk 23. Net Asset Value Economics MARKETS & MARKET FAILURE 1. The economic problem 2. Productive and allocative efficiency 3. Money and exchange 4. Price determination 5. The money market 6. Introduction to the labour market 7. The determinants of demand 8. Supply and elasticity of supply 9. Excess supply and excess capacity 10. Elasticity of demand 11. Market structures 12. Income and cross elasticity 13. Market failure 14. Factor immobility 15. Public and private goods 16. Merit and non-merit goods 17. Cost-benefit analysis 18. Competition policy 19. Market failure and government intervention History ANCIENT HISTORY 1. Prehistory of Greece 2. Mycenae, the Heroic Age c.1550—1125 BC 3. The Greek Middle Ages c.1125—c.700 BC 4. The Greek Tyrannies c. 650—510 BC 5. Sparta 6th and 7th centuries BC 6. Athens and Solon 7. The early inhabitants of Italy 8. The Etruscans 9. Early Roman History up to Tarquin GERMANY & EUROPE 1870—1939 1. Social Change from 1870 to 1914 2. Socialism in Europe 1870 to 1914 3. The Balance of Power in Europe 1870 4. Anti Semitism in Europe 1870 to 1914 5. The Structure of Wilhelmine Germany 6. Bismarck and the Alliance System 7. Weltpolitik 8. Colonial Rivalries 9. First and Second Moroccan Crises 10. The First World War triggers 11. The Causes of the First World War 12. Germany and the First World War 13. Military history of the First World War 14. The Treaty of Versailles 15. The Domestic Impact of the First World War 16. The German Revolution 17. The Weimar Republic 18. The Early Years of the Nazi Party 19. The Rise of the Nazi Party 20. The Establishment of the Nazi Dictatorship 21. Nazi Rule in Germany 1934 to 1939 22. The Economics of the Third Reich 23. Appeasement RUSSIA & EUROPE 1855—1953 1. Alexander II and the Great Reforms 2. Imperial Russia under Alexander III 3. Nicholas II and the 1905 revolution 4. Social and economic developments in Russia 5. Russia: the Great war and collapse of Tsarism 6. Provisonal Government & October Revolution 7. The Era of Lenin 8. The Development of Lenin's Thought 9. New Economic Policy and the Rise of Stalin 10. Stalin and the Soviet Union 1924 to 1953 11. Stalin and the Soviet Economy 12. Stalin and International Relations BRITAIN 1914—1936 1. The Great War and Britain 1914—15 2. Britain during the Great War, 1915—16 3. Lloyd George & the Great War, 1916—1918 4. Great Britain after the War, 1918—22 5. British Politics, 1922—25 6. Class Conflict & the National Strike, 1926 7. Britain & International Relations, 1925—29 8. Social Trends in Britain during the 1920s 9. Social Issues during the late 1920s 10. British Politics 1926—29; Election of 1929 11. Britain — the crisis of 1929 12. The Labour Government of 1929—31 13. Britain and economic affairs, 1931—33 14. Britain and Foreign Affairs, 1931—36 15. Social Conditions in Britain during the 1930s Advanced level Mathematics ALGEBRA & GEOMETRY 1. Simultaneous Equations 2. Polynomial Algebra 3. Cartesian Coordinates 4. The equation of the straight line 5. Intersection of lines and curves 6. Remainder and Factor Theorems 7. Functions 8. Quadratic Inequalities 9. Graphs of Inequalities 10. Indices 11. Polynomial Division 12. Velocity-Time Graphs 13. Tally Charts 14. Absolute and relative errors 15. Sequences and Series 16. Arithmetic Progressions 17. Proof by Contradiction 18. Geometric Progressions 19. The Cartesian Equation of the Circle 20. Transformations of graphs 21. Plane Trigonometry 22. Modulus 23. Trigonometric Functions 24. Inverse Trigonometric Functions 25. Linear Inequalities 26. Proportionality 27. Probability 28. Surds 29. Special Triangles 30. Quadratic Polynomials 31. Roots & Coefficients of Quadratics 32. Radian measure 33. Permutations and Combinations 34. Set Theory and Venn Diagrams 35. Sine and cosine rules 36. Elementary Trigonometric Identities 37. Roots and curve sketching 38. Graphs and roots of equations 39. Picards Method 40. Small Angle Approximations 41. Simultaneous equations in three unknowns 42. Linear relations and experimental laws 43. Conditional Probability 44. Pascal's Triangle and the Binomial Theorem 45. Index Equations and Logarithms 46. The Binomial Theorem for Rational Indices 47. Exponential Growth and Decay 48. Exponential and Natural Logarithm 49. Compound Angle Formulas 50. Sinusoidal functions 51. Vector Algebra 52. The Vector Equation of the Straight Line 53. The Scalar Product of Vectors 54. Axiom Systems 55. Introduction to Complex Numbers 56. The algebra of complex numbers 57. Complex Numbers and the Argand plane 58. De Moivres Theorem 59. Eulers formula 60. Further loci of complex numbers 61. Further graph sketching 62. Mathematical Induction 63. Proof of the Binomial Theorem 64. Polar Coordinates 65. Conic sections 66. Partial Fractions 67. First-order linear recurrence relations 68. Summation finite series with standard results 69. Method of differences 70. Trigonometric Equations 72. Series Expansion 73. Lagrange Interpolating Polynomial 74. Error in an interpolating polynomial 75. Abelian groups 76. Geometrical uses of complex numbers 77. Cyclic Groups 78. The Cayley-Hamilton Theorem 2x2 Matrices 79. Cayley Theorem 80. Determinants 81. Isomorphisms 82. Lagrange theorem 83. Properties of groups 84. Group structure 85. Subgroups 86. Homomorphisms 87. Matrix Algebra 88. Determinant and Inverse of a 2x2 matrix 89. Gaussian elimination 90. Matrix representation of Fibonacci numbers 91. Matrix groups 92. Inverse of a 3 x 3 Matrix 93. Singular and non-singular matrices 94. Properties of Matrix Multiplication 95. Induction in Matrix Algebra 96. Properties of Determinants 97. Permutation groups 98. First Isomorphism Theorem for Groups 99. Roots of Polynomials of Degree 3 100. Scalar Triple Product 101. Systems of Linear Equations 102. Matrix Transformations 103. Mappings of complex numbers 104. Cross product of two vectors 105. Vector planes 106. Eigenvalues and Eigenvectors CALCULUS 1. Introduction to the Differential Calculus 2. Stationary points and curve sketching 3. Applications of Differentiation 4. Differentiation from First Principles 5. The Trapezium Method 6. Integration 7. Direct Integration 8. Applications of integration to find areas 9. Graphs of Rational Functions 10. Derivatives of sine and cosine 11. Products, Chains and Quotients 12. Volumes of Revolution 13. Exponential and Logarithmic Functions 14. Integration by Parts 15. Parametric Equations 16. The Integral of 1/x 17. Integration by Substitution 18. Implicit Differentiation 19. Formation of a differential equation 20. Separation of variables 21. Integrals of squares of trig functions 22. Maclaurin Series 23. Techniques of Integration 24. Integrating Factor 25. The Newton-Raphson formula 26. Errors in Numerical Processes 27. Roots and Recurrence Relations 28. Derivatives of Inverse Trig. Functions 29. Second order homogeneous equations 30. Second order inhomogeneous equations 31. Implicit differentiation — second derivative 32. Integrands to inverse trigonometric functions 33. Integrands to logarithmic function 34. Integration of Partial Fractions 35. Logarithms and Implicit Differentiation 36. Implicit differentiation and MaClaurin series 37. Separation of variables by substitution 38. Trigonometric Substitutions for Integrals 39. Truncation Errors 40. Euler and Trapezoidal Method 41. Numerical methods for differential equations 42. Simpson Method 43. Proof of Simpson Formula 44. Richardson Extrapolation 45. Arc length of a curve in Cartesian coordinates 46. Arc length of a curve in Polar coordinates 47. Arc length of a curve: Parametric form 48. Curves in Euclidean space 49. Functions and continuity 50. The gradient of a scalar field 51. The derivatives of the hyperbolic functions 52. Hyperbolic Functions 53. Inverse Hyperbolic Functions 54. Hyperbolic Identities 55. Integrals with inverse hyperbolic functions 56. Reduction formulae 57. Simultaneous differential equations 58. Surface of Revolution 59. Vector differential calculus 60. Scalar Fields and Vector Functions STATISTICS & PROBABILITY 1. Central Tendency: Mean, Median and Mode 2. Standard Deviation 3. Cumulative Frequency 4. Discrete Random Variables 5. Mutually exclusive and independent events 6. The Binomial Distribution 7. The Normal Distribution 8. Standardised Normal Distribution 9. Regression Lines 10. Correlation 11. The Geometric Distribution 12. Hypothesis Testing — Binomial Distribution 13. Index Numbers 14. Time Series Analysis 15. Bayes Theorem 16. Confidence interval mean — known variance 17. The Central Limit Theorem 18. Pearsons product moment correlation 19. Spearmans Rank Correlation Coefficient 20. Hypothesis Testing — Normal Distribution 21. The Poisson Distribution 22. The Normal Approximation to the Binomial 23. The Normal Approximation to the Poisson 24. The Poisson Approximation to the Binomial 25. Type I and type II errors 26. Scalar multiples of a Poisson variable 27. Test for the Mean of a Poisson distribution 28. Random Number Sampling 29. Estimating Population Parameters 30. Random Samples and Sampling Techniques 31. The Concept of a Statistic 32. Hypothesis test for the population variance 33. Central Concepts in Statistics 34. Continuous Probability Distributions 35. Modeling: Chi squared goodness of fit 36. Chi squared test for independence 37. Degrees of Freedom 38. Difference Sample Means Unknown Variance 39. Moment generating functions 40. Probability generating functions 41. Linear Combinations of Random Variables 42. Maximum Likelihood Estimators 43. Wilcoxon signed rank test on median 44. Non-parametric significance tests 45. Single-sample sign test of population median 46. Paired-sample sign test on medians 47. Paired sample t-test for related data 48. Paired sample Wilcoxon signed rank test 49. Difference of two sample means 50. Pooled sample estimate 51. Testing the Sample Mean 52. The Uniform Distribution MECHANICS 1. Velocity-Time and Displacement-Time Graphs 2. Force diagrams 3. Representation of Forces by Vectors 4. Static Equilibrium 5. Equilibrium of coplanar forces 6. Weight and Free Fall 7. Normal Reaction and Friction 8. Newtons First and Second Laws 9. Relative Motion 10. Projectiles 11. Calculus and Kinematics 12. Motion of a Particle: Vector calculus form 13. Work 14. Energy Conversions 15. Gravitational potential and kinetic energy 16. Connected Particles 17. Moments 18. Linear momentum 19. Power 20. Hookes Law 21. Simple Harmonic Motion 22. Simple Harmonic Motion and Springs 23. Calculus, Kinematics in Three Dimensions 24. Sliding, toppling and suspending 25. Impulsive Tensions in Strings 26. Angular Velocity 27. Motion in a Horizontal Circle 28. Centre of Mass of a Uniform Lamina 29. Motion in a Vertical Circle 30. Motion under a Variable Force 31. Conservation of Angular Momentum 32. Centre of Mass of a Composite Body 33. Motion under a central force 34. Centre of Mass of a Uniform Lamina 35. Centre of Mass Uniform Solid of Revolution 36. Equilibrium of Rigid Bodies in Contact 37. Damped Harmonic Motion 38. Moment of Inertia 39. Impulse, elastic collisions in one dimension 40. Parallel and Perpendicular Axis Theorems 41. Motion described in polar coordinates 42. Simple pendulum 43. Compound pendulum 44. Stability and Oscillations 45. Vector calculus 46. Linear Motion of a Body of Variable Mass DISCRETE & DECISION 1. Algorithms 2. Introduction to graph theory 3. Dijkstra algorithm 4. Sorting Algorithms 5. Critical Path Analysis 6. Dynamic Programming 7. Decision Trees 8. The Maximal Flow Problem 9. The Hungarian algorithm 10. Introduction to Linear Programming 11. Simplex Method 12. Matching Problems 13. Game Theory 14. Minimum connector problem 15. Recurrence relations 16. Proofs for linear recurrence relations 17. Simulation by Monte Carlo Methods 18. Travelling and Optimal Salesperson Problems 19. The Travelling Salesperson Problem Philosophy INTRODUCTION TO PHILOSOPHY 1. The problem of evil 2. Introduction to Plato 3. Knowledge, belief and justification 4. Descartes Meditation I 5. Introduction to the problem of universals 6. Introduction to metaethics 7. Subjectivism versus objectivism 8. Aristotle's function argument 9. Natural Law Theory 10. Utilitarianism 11. The Nicomachaen Ethics of Aristotle 12. Virtue Ethics 13. Descartes Meditation II 14. Hume and empiricism 15. The paradox of induction 16. Hume's attack on Descartes 17. The Cosmological Argument 18. The Ontological Argument 19. The Teleological Argument 20. The Argument from religious experience 21. The Moral Argument 22. The argument from illusion 23. Materialism 24. Human Identity Sociology PERSPECTIVES & METHODOLOGY 1. Introduction to Marxism 2. Introduction to Durkheim 3. Weber: classes, status groups and parties 4. Introduction to patriarchy and gender roles 5. Mass culture theory 6. The Frankfurt school STRATIFICATION & DIVERSITY 1. Ethnic groups and discrimination 2. Race, Ethnicity and Nationalism 3. Social Inequality 4. Theories of Racism 5. Class structure 6. Modern Functionalism and Stratification 7. Social Mobility 8. Bottomore: Classes in Modern Britain 9. American exceptionalism ASPECTS OF SOCIETY 1. Definitions of Poverty 2. Theories of Poverty 3. Solutions to Poverty 4. Alienation 5. Leisure 6. Work and Technological Change 7. Conflict and Cooperation at Work 8. Attitudes to Work 9. Unemployment 10. Perspectives on Education 11. Education and Ethnicity 12. Education and Gender 13. The Family and Social Structure 14. The Family and Household Structure 15. Conjugal Roles 16. Marital Breakdown 17. Post War Education in Britain 18. British Social Policy 1945—1990