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Alpha Plus got incepted in Delhi in the year 2003 at various locations to cater the needs of Mathematics and Actuarial aspirants. Today Alpha Plus become a name synonym to academic excellence and is a hallmark of success for Mathematics and Actuarial aspirant. Also It has produced excellent results year after year since 2003 and till this year trend is continued. Our commitment towards the success of student is achieved due to the unique academic system & teaching methodologies which completely takes care of Graduation syllabus, other features includes practice test, Special Doubt Clearing Session, Micro & Macro Level analysis to give Regular feedback to students etc. Alpha Plus has a huge pool of good faculties, which ensures that our system is immune to any faculty movement and also we are able to incorporate any change in system immediately. Thus, undisrupted quality teaching has become inherent feature of our academic system. This has already been proven through our unmatched results year after year. Incorporate the years of experience in formulating a comprehensive learning environment that solidifies the strengths of students and makes them ready for the tough challenge of examinations. Discover and rejuvenate the unique qualities of each student, motivating them to respect their own special abilities and those of others. Honour sensitivity, ethical behaviour, trust and compassion and nurture these qualities in the Alpha Plus Family. Embrace diversity through instructions and examples; foster understanding of the full spectrum of human social and cultural differences. Commit to the principle of serving, teaching the grace of giving, the warmth of community, and the dignity of a cooperative spirit. To maintain high academic standards, teaching quality, promote the analytical thinking and independent judgement necessary to function responsibility. CSIR-UGC National Eligibility Test (NET) UNIT–1: Analysis:Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem. Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples. Linear Algebra:Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations. Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear transformations. Change of basis,
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