Topics: Discrete mathematics, logic, sets, functions, sequences, matrices, algorithms, Number theory, cryptography, induction, recursion, counting, discrete probability, advanced counting techniques, counting techniques, Linear Recurrence Relations, modelling computation, Finite-State Machines, relations, graphs, trees, boolean algebra, modelling computation, Boolean Functions, Logic Gates, Minimization of Circuits.Tree Traversal, Spanning Trees, Minimum Spanning Trees, Graph Models, Graph Terminology, Graph Isomorphism, Connectivity, Euler path, Hamilton Path, Shortest-Path Problems, Planar Graphs, Graph Coloring, Representing Relations, Equivalence Relations, Probability Theory, Bayes Theorem, variance, Pigeonhole Principle, permutation combination, binomial coefficient, Recursive Algorithms, Program Correctness, Divisibility, Modular Arithmetic, Integer Representations, Set Operations, Cardinality of Sets

Topics: Applied Mechanics, force, force systems, free body diagrams, resultant force, moments, Varignon’s Theorem, centre of gravity, centroid, Moment of Inertia, friction, Screw Friction, rectilinear motion, Velocity-Time Graphs, Displacement-Time Graphs, laws of motion, impulse, D’alembert’s Principle, work, power, energy, simple machine, Weston’s Differential Pulley Block, circular motion, Centrifugal force, Centripetal Force, curvilinear motion, stress, strain, Hooke's law, tensile test, Strain Hardening, Poisson’s Ratio

Topics: elements, compounds, atomic theory, chemical reaction, atom constituents, chemical symbols, chemical formulae, chemical reactions, chemical equations, electronic configuration, atomic number, mass numbers, nuclear atom, electronic, energy levels, Ion formations, nuclear reactions, radioactivity, nuclear radiations, nuclear fusion, nuclear fission, radioactivity hazards, chemical bonding, electrovalent bonding, Ionic bonding, electrovalent compounds, covalent bonding, covalent compounds, coordinate covalent bonding, dative covalent bonding, metallic bonding, intermolecular bonding, Van der Waal's forces, dipole-dipole attractions, hydrogen bonding, periodic table, periodic law, transition elements, atomic orbital model, principal quantum number, subsidiary quantum number, azimuthal quantum number, magnetic quantum number, spin quantum number, atomic orbital shape, atomic size, ionic radius, ionization energy, electron affinity, electronegativity, mole concept, melting, vaporization, boiling point, evaporation sublimation, heating graphs, cooling graphs, Boyle's law, Charles's law, Avogadro's law, boiling, solid classification, solid properties, molecular solid, metallic solid, Ionic solid, covalent solid, energy changes, heat content, heat of reaction, exothermic reactions, energy level diagrams, standard state, thermochemical equations, entropy, entropy change, free energy, chemical kinetic, rate of a chemical reaction, temperature, gas pressure, catalyst, activation, reaction rate, collision theory, Le Chatelier's principle, Haber process, contact process, salt hydrolysis, buffer solutions, common Ion effect, solubility product, Acid bases, salt, electrolysis, redox reactions, electrolytic conduction, oxidation, reduction, copper purification, electroplating, quantitative hydrolysis, metal corrosion, iron rusting, carbon, carbon allotropes, Diamond graphite, amorphous carbon, combustion reactions, industrial gas chemistry, metals, alloys, chemical industry, heavy chemicals, fine chemicals, fertilizers, plastics, soaps, detergents, pharmaceuticals, Nigerian chemical industry, aromatic compounds, Alicyclic compound, heterocyclic compound, homologous series, functional groups, isomerism, structural isomerism, geometric isomerism, IUPAC Nomenclature of organic compounds, purification methods, distillation, crystallization, chromatography, empirical formula, molecular formular, alkanes, natural gas, petroleum crude oil, benzene, fractional distillation petrol quality, cracking, isomerization, petrochemicals, alkanols, alkanoic acid, alkenoate, fat, oils, amino acid, polymer chemistry, polymerization processes, condensation polymerization, resins, natural polymers, carbohydrates, proteins, synthetic polymers, water pollution

Topics: algebra, numbers, fractions, inequalities, cartesian plane, vector algebra, linear equations, trigonometry, trigonometric rations, trigonometric graphs, Pythagorean Identities, functions, Exponential Functions, Absolute Value Function, rational functions, root functions, Piecewise Defined Functions, limits, continuity, Horizontal Asymptotes, differential calculus, Derivative Functions, Tangent Line Problems, chain rule, Euclidean Geometry, Spherical Trigonometry

Topics: Computer Algorithms, pseudocode conventions, recursive algorithms, performance analysis, randomized algorithms, primality testing, elementary data structures, binary search trees, cost amortization, prority queues, sets, graphs, graph representation, merge sort, quick sort, Strassen's matrix multiplication, convex hull, greedy method, knapsack problem, tree vertex splitting, prim's algorithm, dynamic programming, reliability design, backtracking, graph coloring, least cost search, algebraic problems, fast Fourier transform, lower bound theory, comparison trees, ordered searching, Cook's theorem, approximation algorithms, absolute algorithms, polynomial time approximation schemes, mesh algorithms, packet routing, hyper algorithms, PPR routing

Topics: discrete mathematics, mathematical logic, functions, proofs, set theory, set operations, axiomatic set theory, real numbers, arithmetic, induction, recursion, summation notation, Asymptotic notation, number theory, graphs, multiplication, exponentiation, binomial coefficients, generating functions, probability theory, random variables, Markov's inequality, probability generating functions, linear algebra, abstract vector spaces, finite fields

Topics: Calculus, Analytic Geometry, real numbers, real line, coordinates, functions, shifting graphs, trignometric functions, rates of change, limits, continuity, tangent lines, derivative of a function, differentiation rules, rates of change, chain rule, derivatives, implicit differentiation, rational exponents, extreme values of functions, mean value theorem, first derivative test, optimization, linearization, differentials, Newton's method, integration, indefinite integrals, differential equations, initial value problems, mathematical modelling, Riemann sums, definite integrals, mean value theorem, fundamental theorem, numerical integration, cylindrical shells, application of integrals, work, fluid pressure, inverse functions, natural logarithms, transcendental functions, L'Hopital's rule, inverse trignometric functions, hyperbolic functions, first order differential equations, Euler's numerical method, Integration formulas, integration by parts, integral tables, infinite series, power series, Maclaurin series, Taylor series, conic sections

Topics: Parameters, Statistics, Statistical data analysis, Variables, organization of the data, tables, graphs, Sample Distributions, Population Distributions

Topics: Scope of Statistics, statistical data, data types, scale of measurements, data collection, survey sampling techniques, Data presentation, Bar Charts, Histogram, polygons, graphs, Errors, approximation, Frequency, relative frequency, cumulative frequency distributions, Measure of location, Measure of dispersion, Skewness, Kurtosis, Rates, Ratios, index numbers, weight quantity, Rates, Ratio, index numbers

Topics: Process control, digital processing, analog processing, process system, semiconductor, thermocouple, signal flow graphs