Exam Pattern & Syllabus for APPSC Mathematics subject Degree Lecturers, APPSC has given the Degree College Lecturers Recruitment notification and online applications are invited online from qualified candidates to the post of Degree College Lecturers in Govt Degree Colleges in the State of Andhra Pradesh.

The proforma Application will be available on the Commission’s Website (www.psc.ap.gov.in) from 29/12/2016 to 28/01/2017 (Note: 27/01/2017 is the last date for payment of fee up- to 11:59 midnight). APPSC Degree College Lecturers Recruitment notification no.26/2016 and apply online now @ http://appscapplications17.apspsc.gov.in/

**Scheme of Exam: **Exam Pattern & Syllabus for APPSC Mathematics subject Degree Lecturers

Papers | No. of Questions | Duration (Minutes) | Maximum Marks |

PART-A: Written ‘Examination (Objective Type) | |||

Paper-1: General Studies & Mental Ability | 150 | 150 | 150 |

Paper-2: Mathematics subject | 150 | 150 | 300 |

PART-B: Interview (Oral Test) | 50 | ||

TOTAL | 500 |

**NEGATIVE MARKS: **

As per G.O.Ms. No.235, Finance (HRI, Plg & Policy) Dept., Dt.06/12/2016, for each wrong answer will be penalized with 1/3rd of the marks prescribed for the question.

**Mathematics Subject Syllabus:** Exam Pattern & Syllabus for APPSC Mathematics subject Degree Lecturers

MATHEMATICS**I. Real Analysis**

Finite, countable and uncountable sets – Real Number system R – infimum and supremum of a subset of R – Bolzano – Weierstrass theorem. Sequences, convergence, limit superior and limit inferior of sequences, subsequences, Heine Borel Theorem. Infinite series – Tests of convergence.

Continuity and uniform continuity of real-valued functions of a real variable. Monotonic functions and functions of bounded variation. Differentiability and mean value theorems. Riemann integrability. Sequences and Series of functions.

**II. Metric Spaces**

Metric spaces – completeness, compactness and connectedness – continuity and uniform continuity of functions from one metric space into another.

Topological spaces – base and subbase – continuous function.

**III. Elementary Number**

Primes and composite numbers – Fundamental Theorem of arithmetic – divisibility– congruences – Fermat’s theorem – Wilson’s Theorem – Euler’s Ǿ – function.

**IV. Group Theory**

Groups, subgroups, normal subgroups – quotient groups – homomorphisms and isomorphism theorems – permutation groups, cyclic groups, Cayley’s theorem. Sylow’s theorems and their applications.

**V. Ring Theory**

Rings, integral domains, fields – subrings and ideals – Quotient rings – homomorphisms – Prime ideals and maximal ideals – polynomial rings – Irreducibility of polynomials – Euclidean domains and principal ideal domains.

**VI. Vector Spaces**

Vector Spaces, Subspaces – Linear dependence and independence of vectors – basis and dimension – Quotient spaces – Inner product spaces – Orthonormal basis – Gram – Schmidt process.

**VII. Matrix Theory**

Linear transformations – Rank and nullity – change of bases. Matrix of a linear transformation – singular and non-singular matrices – Inverse of matrix – Eigenvalues and eigenvectors of a matrix and of linear transformation – Cayley – Hamilton’s theorem.

**VIII. Complex Analysis**

Algebra of complex numbers – the complex plane – Complex functions and their Analyticity – Cauchy-Riemann equations – Mobius transformations. Power Series. Complex Integration – Cauchy’s theorem – Morera’s Theorem – Cauchy’s integral formula – Liouville’s theorem – Maximum modules principle – Schwarz’s lemma – Taylor’s series – Laurents series.

Calculus of residues and evaluation of integrals.

**IX. Ordinary Differential Equation**

Ordinary Differential Equation (ODE) of the first order and first degree – Different methods of solving them – Exact Differential equations and integrating factors. ODE of the first order and higher degree – equations solvable for p, x, and y – Clairaut’s equations – Singular Solutions.

Linear differential equations with constant coefficients and variable coefficients – a variation of parameters.

**X. Partial Differential Equations**

Formation of differential equations (PDE) – Lagrange and Charpit methods for solving first order – PDE’s – Cauchy problem for first-order PDE’s Classification of second-order PDE’s – General solution of higher-order PDE’s with constant coefficients. **Check more details from here**