Organisation : Telangana Public Service Commission
Announcement : Syllabus
Designation : Degree Lecturer
Degree Lecturer Syllabus :
Paper : General Studies, General Abilities and Basic Profeiciency in English
Section I : General Studies
1. Current Affairs – Regional, National & International.
2. Indian Constitution; Indian Political System; Governance and Public Policy.
Related / Similar Syllabus : TSCHE EAMCET Syllabus 2021
3. Social Exclusion; Rights issues such as Gender, Caste, Tribe, Disability etc.and inclusive policies.
4. Society Culture, Civilization Heritage, Arts and Literature of India and Telangana
5. General Science; India’s Achievements in Science and Technology
6. Environmental Issues; Disaster Management- Prevention and Mitigation Strategies and Sustainable Development.
7. Economic and Social Development of India and Telangana.
8. Socio-economic, Political and Cultural History of Telangana with special emphasis on Telangana Statehood Movement and formation of Telangana state.
Section II : General Abilities
9. Analytical Abilities: Logical Reasoning and Data Interpretation.
10. Moral Values and Professional Ethics in Education.
11. Teaching Aptitude
Section III : Basic Proficiency in English
i) School Level English Grammar:Articles; Tense; Noun & Pronouns; Adjectives; Adverbs; Verbs; Modals; Subject-Verb Agreement; Non-Finites; Reported Speech; Degrees of Comparison; Active and Passive Voice; Prepositions; Conjunctions; Conditionals.
ii) Vocabulary: Synonyms and Antonyms; Phrasal Verbs; Related Pair of Words; Idioms and Phrases; Proverbs.
iii) Words and Sentences : Use of Words ; Choosing Appropriate words and Words often Confused; Sentence Arrangement, Completion, Fillers and Improvement; Transformation of Sentences ; Comprehension; Punctuation; Spelling Test; Spotting of Errors.
Main Exam Syllabus :
I. Real Analysis :
Finite, Countable and Uncountable sets – Real Number system R – Infimum and Supremum of asubset of R – Bolzano- Weierstrass Theorem- Sequences- Convergence- Limit Superior and LimitInferior of a Sequence- Sub sequences- Heine
Borel Theorem- Infinite Series – Tests of Convergence-Continuity and Uniform continuity of a real valued function of a real variable- Monotonic Functions- Functions of Bounded Variation- Differentiability and Mean Value Theorems- Riemann Integrability-Sequences and Series of Functions
II. Metric Spaces :
Metric spaces – Completeness- Compactness- Connectedness – Continuity and Uniform continuity ofa function from one metric space into another-Topological Spaces – Bases and Subbases – Continuousfunctions
III. Elementary Number Theory :
Primes and Composite numbers – Fundamental Theorem of Arithmetic – Divisibility – Congruences– Fermat’s theorem – Wilson’s Theorem – Euler’s Phi – Function
IV. Group Theory :
Groups- Subgroups- Normal Subgroups- Quotient groups- Homomorphisms- IsomorphismTheorems-Permutation groups- Cyclic groups- Cayley’s theorem.Sylow’s theorems – Their applications
V. Rings and Fields :
Rings- Integral domain- Fields- Subrings – Ideals – Quotient rings – Homomorphisms – Prime ideals-Maximal ideals – Polynomial rings – Irreducibility of polynomials – Euclidean domains- Principalideal domains-Algebraic, Normal, Separable extensions of fields- Galois Theory
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. Functional Analysis :
Normed Linear Spaces- Banach Spaces -Inner Product Spaces- Hilbert Spaces-Linear Operators- LinearFunctionals- Open Mapping Theorem- Closed Graph Theorem- Uniform Boundedness theorem- Hahn– Banach Theorem
VIII. Theory of Matrices :
Linear Transformations – Rank and nullity – Change of bases- Matrix of a Linear Transformation –Singular and Non-singular matrices – Inverse of a matrix – Eigenvalues and Eigenvectors of a matrixand of a Linear Transformation – Cayley- Hamilton’s theorem- Quadratic forms- Signature and Index