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# tspsc.gov.in Degree Lecturer Syllabus : Telangana Public Service Commission

** Organisation **: Telangana Public Service Commission

**: Syllabus**

__Announcement__**: Degree Lecturer**

__Designation__** Website **: http://tspsc.gov.in/TSPSCWEB0508/

**: http://www.syllabus.gen.in/uploads/1498-DL.pdf**

__Download Syllabus Here__## 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: College Librarian Exam Syllabus Telangana Public Service Commission : www.syllabus.gen.in/1493.html

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 **:

**:**

__Maths__**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