1. Algebra -Groups, semi -groups, Lagranges theorem. Cyclic groups, Normal sub-groups Quotient groups, conjugate elements and sub- groups rings sub-rings, Integral domain, Fields and polynomial rings.
   
   Vector spaces, Linear independence bases Dimensions of a finitely generated space. Lineartransformation. Matrices and their operations. Row & column reduction Echelon form, Rank and nullity of a linear transfoamation. System of linear equations.



2. Differential Calculus - Convergence of sequences and series; Limit and continuity of functions. Differentiability,
   Mean Value theorem. Taylor's theorem. Expansion in Taylor's and Maclauries Series, Maxima and Minima, successive differentiation. Leibnitz's theorem. Functions. of several variables Partial derivatives, transformation. Eular's theorem.jacobian.



3. Integral Calculus - Integration of rational , irrational and transcendental functions. Definite integrals; Double and tripe integrals, Beta and Gamma functions.



4. Differential Equations - Ordinary differential equations of first and higher degree Homogeneous equations of first degree Integrating factors; Linear differential equations with constant co-efficients. Complimentary functions and particular integrais, Linear differential equations with variable co-efficients.



5. Vector Analysis - Algebra of vectors , Double and triple products (Scalar and Vectors ) , Differentiation of vectors, Directional direvatives Gradient divergence and curl and their elementary properties. Integratioin of vector functions along curves.



6. Statistics - Statistical population and random sample Collection, and presentation of data measures of locaton dispersion Moments and shepard's corrections, cummulants. Measures of skewness and kurtosis.

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1. Analytical Geometry- Direction cosines, plane and straight line, sphere cone and cylinder. Tangent planes and normal lines.



2. Advanced Calculus -Tangents and Normals. Asymptotes Curvature and Tracing of conics. Determination of areas, lengths surfaces and volumes (Cartesian and polar curves)



3. Real Analysis - Least upper bound and greatest lower bounds of sets; limit point of a set . Bolzanoweirstrass theorem. open and closed sets and their porperties, Metric spaces. Cauchy sequences and complete metric spares . Compact sets and Heine-Borel theorem.



4. Boolean Algebra - Difinition and properties. Demorgan's Laws. Switching circuits. Boolean fuctions conjunctive and disjunctive forms.



5. Mechanics - Equilibrium of three forces, friction. Newton's second law of motion, impulsive force. kinetic energy of particles angular velocity, tragential and normal velocity and accleration projectiles on horizontal and inclined planes Colliston of elastic bodies, Direct and bolique impacts.



6. Partial Differential Equations - Partial differential equations of first order, Standards forms, Linear partial differential equations of higher degree with constant co-efficients. Laplace, diffusion and vibration equation. Simple cases of solutions of these equations as boundary value problems.