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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