Subject-wise Syllabus & Books for UPSC Optional Mathematics

UPSC Optional Mathematics PAPER – I

(1) Linear Algebra: 

• Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; row and column reduction, echelon form, congruence, and similarity; the rank of a matrix; the inverse of a matrix; solution of a system of linear equations; eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices, and their eigenvalues.
• Books:
  • SCHAUM SERIES – Seymour Lipschutz 
  • LINEAR ALGEBRA – Hoffman and Kunze 

(2) Calculus: 

• Real numbers, functions of a real variable, limits, continuity, differentiability, mean value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; curve tracing; functions of two or three variables: limits, continuity, partial derivatives, maxima, and minima, Lagrange’s method of multipliers, Jacobian. Riemann’s definition of definite integrals; indefinite integrals; infinite and improper integrals; double and triple integrals (evaluation techniques only); areas, surface, and volumes.
• Books:
  • MATHEMATICAL ANALYSIS – S C Malik and Savita Arora
  • ELEMENTS OF REAL ANALYSIS – Shanti Narayan and M D Raisinghania

(3) Analytic Geometry: 

• Cartesian and polar coordinates in three dimensions, second-degree equations in three variables, reduction to canonical forms, straight lines, the shortest distance between two skew lines; plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets, and their properties.
• Books:
  • ANALYTICAL SOLID GEOMETRY – Shanti Narayan and P K Mittal
  • SOLID GEOMETRY – P N Chatterjee

(4) Ordinary Differential Equations: 

• Formulation of differential equations; equations of the first order and first degree, integrating factor; orthogonal trajectory; equations of first order but not of the first degree, Clairaut’s equation, singular solution. Second and higher-order linear equations with constant coefficients, complementary functions, particular integrals, and general solutions. Second-order linear equations with variable coefficients, Euler-Cauchy equation; determination of complete solution when one solution is known using the method of variation of parameters. Laplace and inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.
• Books:
  • ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS – M D Raisinghania

(5) Dynamics & Statics: 

• Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; work and energy, conservation of energy; Kepler’s laws, orbits under central forces. Equilibrium of a system of particles; work and potential energy, friction; common catenary; the principle of virtual work; stability of equilibrium, equilibrium of forces in three dimensions.
• Books:
  • KRISHNA SERIES 

(6) Vector Analysis: 

• Scalar and vector fields, differentiation of vector field of a scalar variable; gradient, divergence and curl in cartesian and cylindrical coordinates; higher order derivatives; vector identities and vector equations. Application to geometry: curves in space, curvature, and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.
• Books:
  • SCHAUM SERIES – Murray R. Spiegel

UPSC Optional Mathematics PAPER-II

(1) Algebra: 

• Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem. Rings, subrings and ideals, homomorphisms of rings; integral domains, principal ideal domains, Euclidean domains, and unique factorization domains; Fields, quotient fields.
• Books:
  • CONTEMPORARY ABSTRACT ALGEBRA – Joseph Gallian

(2) Real Analysis: 

• Real number system as an ordered field with the least upper bound property; sequences, the limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals; fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability, and integrability for sequences and series of functions; partial derivatives of functions of several (two or three) variables, maxima, and minima.
• Books:
  • MATHEMATICAL ANALYSIS – S C Malik and Savita Arora
  • ELEMENTS OF REAL ANALYSIS – Shanti Narayan and M D Raisinghania

(3) Complex Analysis: 

• Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, Taylor’s series; singularities; Laurent’s series; Cauchy’s residue theorem; contour integration.
• Books:
  • SCHAUM SERIES – Speigel, Lipschitz, Schiller, Spellman

(4) Linear Programming: 

• Linear programming problems, basic solution, basic feasible solution, and optimal solution; graphical method and simplex method of solutions; duality. Transportation and assignment problems.
• Books:
  • LINEAR PROGRAMMING AND GAME THEORY – Lakshmishree Bandopadhyay

(5) Partial differential equations: 

• Family of surfaces in three dimensions and formulation of partial differential equations; solution of quasilinear partial differential equations of the first order, Cauchy’s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; equation of a vibrating string, heat equation, Laplace equation, and their solutions.
• Books:
  • ADVANCED DIFFERENTIAL EQUATIONS – M D Raisinghania 

(6) Numerical Analysis and Computer programming: 

• Numerical methods:
  • solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi, and Newton-Raphson methods; solution of a system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods. Newton’s (forward and backward) interpolation, and Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runge Kutta-methods.
• Computer Programming:
  • Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers. Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals, and long integers. Algorithms and flow charts for solving numerical analysis problems.
• Books:
  • COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES – M.Goyal
  • NUMERICAL METHODS – Jain, Iyengar, and Jain 
  • DIGITAL LOGIC AND COMPUTER DESIGN – M. Morris Mano

(7) Mechanics and Fluid Dynamics: 

• Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions. Equation of continuity; Euler’s equation of motion for inviscid flow; Stream-lines, the path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.
• Books:
  • KRISHNA SERIES

Free Courses for UPSC Optional Mathematics

• Visit www.youtube.com/tripbohemia
• Free Linear Algebra Course: Link to the Video Lectures
• Free Real Analysis Course: Link to the Video Lectures

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Subject-wise Book List for HTET Exam 

For all levels ie PRT (I Level), TGT (II Level), and PGT (III Level) the following books shall be necessary and sufficient (ie. very helpful)

• Child Development and Pedagogy:
  • RBD Publication
• English:
  • Wren & Martin
  • Class IX or X Grammar Book
  • SP Bakshi (Arihant Publication)
• Hindi:
  • Hindi Vyakran Book ( Class VIII or Class IX )
  • Diamond Publication
• General Intelligence and Reasoning Ability:
  •  Dr. R.S. Agarwal ( S Chand Publication )
• Quantitative Aptitude:
  • Dr. R.S. Agarwal ( S Chand Publication )
• Haryana G.K.:
  • Know Your State Haryana
• Mathematics:
  • R D Sharma Objective Mathematics
  • Books for DSSSB Mathematics
  • Class X-XII NCERTs

Exam Pattern

Exam Pattern Varies slightly as per the three different levels of the HTET examination. It has been detailed level-wise as follows:

PRT ( I Level )

TGT ( II Level )

PGT ( III Level )

Syllabus

1. Child Development and Pedagogy 
   • In Child Development and Pedagogy, Child psychology focuses on the mind and behavior of children from parental development through adolescence. Child psychology deals with the growth of children physically, mentally, and emotionally, and it also helps in social development.
     • Child Development
       • Growth & development and its relationship with learning
       • Heredity & Environment
       • Socialization processes, Piagel
     • Theories
       • Jean Piaget’s Moral Development Theory
       • Bruner’s Theory of Cognitive Development Theory
       • Kohlberg’s Moral Development Theory
       • Havighurst’s Moral Development Theory
       • Vygotsky’s Socio-Cultural Development Theory
       • Erickson’s Theory of Psychosocial Development
       • Bronfenbrenner’s Ecological Theory
       • David Elkind’s Theory of Adolescence Egocentrism
     • Kohlberg, and Vygotsky
       • Constructs and critical perspectives
       • Concepts of child-centered and progressive education
       • Multi-Dimensional Intelligence, Language & Thought
       • Gender roles, gender-bias and educational practice
       • Individual differences among learners
       • Assessment & Evaluation
       • Formulating appropriate questions
       • Critical thinking in the classroom, and for assessing learner achievement.
     • Inclusive education
       • Understanding children with special needs
       • Diverse backgrounds including disadvantaged and deprived & Talented
       • Creative, Specially abled Learners
     • Learning and Motivation
       • Basic processes of teaching and learning
       • Strategies of learning
       • Understanding children’s ‘errors’
       • Cognition & Emotions, Motivation, and learning
         
2. Language-Hindi
   • हिंदी भाषा परिचय
   • संज्ञा
   • सर्वनाम
   • विशेषण
   • क्रिया
   • वचन
   • लिंग
   • वाच्य
   • अव्यय
   • पदबंध
   • संधि
   • उपसर्ग एवं प्रत्यय
   • वाक्य निर्माण (सरल, संयुक्त एवं मिश्रित वाक्य)
   • पर्यायवाची
   • काल
   • विपरीपार्थक
   • अनेकार्थक
   • समानार्थी शब्द
   • मुहावरे एवं लोकोक्तियाँ
   • अलंकार
   • तत्सम, तद्भव
   • देशज एवं विदेशी शब्द
   • समास
     
3. Language-English
   • Articles
   • Adverbs (Types)
   • Modals
   • Syntax (Subject Verb Agreement)
   • Narration
   • Pronouns
   • Adjective (Degree)
   • Verb
   • Prepositions
   • Tenses
   • Punctuation
   • Voice (Active & Passive)
   • Vocabulary
     • One Word
     • Idioms
     • Antonym & Synonyms
   • Phrases
   • Figures of Speech
   • Sentences (Conditional Sentences)
   • Clauses
     
4. Quantitative Aptitude
   • Number System, Fractions
   • Algebra, Ratio, and Proportion
   • Understanding Elementary Shapes (2-D and 3-D)
   • Mensuration, Profit & loss
   • Average, problem on age
   • Speed distance &Time
   • Percentage, SI & CI
   • Time & Work
     
5. Reasoning
   • Analogies, similarities
   • Syllogism, space visualization
   • Problem-solving, Blood Relation
   • Arithmetical reasoning
   • Figure classification
   • Logical Reasoning
     
6. Haryana GK
   • Haryana districts
   • Stadium, culture
   • Folk dance, food
   • All historical places, etc.
     
7. Mathematics 
   • Complex Numbers
   • Series
     • Arithmetic Progression (AP)
     • Geometric Progression (GP)
     • Harmonic Progression (HP)
   • Functions
   • Binomial Theorem
   • Coordinate Geometry
   • Trigonometry
     • Trigonometric Ratios & Identities
     • Properties of Triangles & Circles Connected with Trigonometry
     • Heights & Distances
     • Trigonometric Equations
   • Probability
   • Calculus
     • Limits
     • Continuity
     • Differentiability
     • Indefinite & Definite Integrals
     • Areas of Bounded Regions
     • Differential Equations
   • Vectors
     • Algebra of Vectors
     • Scalar Product of 2 vectors & 3 vectors
     • Vector Product of 2 vectors & 3 vectors
   • Three Dimensional Geometry
     • 3-D Coordinate System
     • Planes & Straight Lines in Space
       
8. Environment Studies 
   • Food: Sources, Components of food
   • Materials, The World of the Living
   • Moving Things People and Ideas
   • How things work, Electric current and circuits
   • Magnets, Natural Phenomena
   • Natural Resources

Free HTET Courses

Visit our Channel: tripBohemia | School Mathematics

Previous Year Papers with Complete Solutions

Visit :

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The Central Board of Secondary Education will organize the 16th edition of the Central Teacher Eligibility Test (CTET) in CBT (Computer Based Test – Online) mode between December 2022 to January 2023.

Presently, The exact date of the examination will be communicated on the admit cards of the candidates.

Information Bulletin

The complete Information Bulletin carrying details of the examination, syllabus, languages, eligibility criteria, examination fee, examination cities, and important dates will be available on CTET’s official website soon.
Henceforth, the aspiring candidates are requested to download the Information Bulletin from the below-mentioned website only and read it carefully before applying.

Mode of Application

Online Mode:
Aspiring candidates have to apply online only through the CTET website i.e. https://ctet.nic.in.

Important Dates

Hence, the online application process will start from 31-10-2022 (Monday) onwards and the last date for submitting an online application is 24-11-2022 (Thursday) up to 23:59 hrs (ie. 11:59 PM).

Application Fess

The fee can be paid up to 25-11-2022 (Friday) before 15:30 hrs (ie. 3:30 PM).

Exam City

The candidates must note that the examination city of their choice will be allotted on first cum first served basis only as per the availability of capacity in the city of examination.

Thereafter, the candidates, who complete the online application process and pay the fee on first cum first served basis, will be allotted the examination city of their choice as per availability in that particular city.

And, the total capacity in a particular city will also be available on the portal. If the total capacity of a particular city is full during the completion of the application process or making payment of the examination fee or the process of updating the transaction on the portal, the candidate will be given the option either to select any other city or cancel the transaction. If a candidate cancels the transaction, the full fee will be refunded to his/her account as per the mode of payment and the application will not be considered for this examination of CTET. The request for a change of examination city will not be accepted in any case.

Important Links for CTET 2022 Exam Registration

• CTET’s official website:
  https://ctet.nic.in

Sources & References

• Official Notice:
  https://cdnbbsr.s3waas.gov.in/s3443dec3062d0286986e21dc0631734c9/uploads/2022/10/2022102017.pdf
• Official Website:
  https://ctet.nic.in/

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This Test is conducted by UGC/CSIR twice a year in June and December.

‘ Joint CSIR UGC NET is a test being conducted to determine the eligibility of Indian nationals for Junior Research Fellowship (JRF) and for Lectureship (LS) /Assistant Professor in Indian universities and colleges subject to fulfilling the eligibility criteria laid down by UGC. ‘

CSIR is the Council of Scientific & Industrial Research and UGC is University Grants Commission.

If any of these questions is worrying you,

‘ What should I go for after NET?’ or, ‘ What will I do after I clear NET, ‘ or, ‘ What are the job opportunities that would open for me after I clear UGC/CSIR NET? ‘, then you are at the right page.

Scroll down to know more.

Career Opportunities After Clearing UGC/CSIR NET Exam

• Continue Study:
  • Ph.D. (Doctorate)
  • Post Doctorate
• Give GATE
• Pursue Research with Scholarships
  • JRF
  • SRF
• Research-related jobs:
  • Mathematician
  • Scientist:
    • Data Scientist
    • Scientific Laboratory Technician
• Recruitments in Public Sector:
  • Universities:
    • TIFR ( Tata Institute of Fundamental Research )
      • Mathematical and Scientific Research
    • IISc ( Indian Institute of Science )
      • Research in science, engineering, design, and management
    • TISS ( Tata Institute of Social Sciences )
      • Research in social work, social sciences, human resources management, health systems, and allied fields
  • Institutions:
    • Pusa Institute ( IARI, The Indian Agricultural Research Institute )
      • Agricultural Research
    • ISRO ( The Indian Space Research Organisation )
      • Space Research
    • IVRI ( Indian Veterinary Research Institute )
      • Research in the field of veterinary medicine and allied branches
  • Departments:
    • DAE ( Department of Atomic Energy )
      • development of nuclear power technology
  • Centers:
    • IGCAR ( Indira Gandhi Centre for Atomic Research )
      • Nuclear Research
    • BARC ( Bhabha Atomic Research Centre )
      • Nuclear Research
• Recruitments in Private Sector:
  • Private Companies
  • Institutions
  • Colleges
  • Universities
• Teaching:
  • Assistant Professor
  • Assistant Lecturer
• Officers

Study Material for UGC/CSIR NET

For one of the best subject wise Video Lectures & Notes: https://books.tripbohemia.com/category/video-lectures-notes/

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The Good News For Assistant Professors is that Ph.D. & NET will not be compulsory from 2023, as is under discussion in UGC updated via tweets this Tuesday.

Guidelines for Engaging Professors of Practice in Universities and Colleges:

” The National Education Policy 2020 seeks to transform higher education by focusing on skill-based education to meet the needs of the industry and the economy. Further, the NEP also recommends integrating vocational education with general education and strengthening industry-academia collaboration in HEIs. For skilling youth at the optimum level, learners are required to think like employers and employers are to think like learners. Towards this, the UGC has taken a new initiative to bring the industry and other professional expertise into the academic institutions through a new category of positions called “Professor of Practice”. This will help to take real-world practices and experiences into the classrooms and also augment the faculty resources in higher education institutions. In turn, the industry and society will benefit from trained graduates equipped with the relevant skills, ” remarks UGC.

News Clippings

Chairman of UGC, Prof. M. Jagadesh Kumar

” Prof. M. Jagadesh Kumar obtained his MS(EE) and Ph.D. (EE) degrees from the Department of Electrical Engineering, Indian Institute of Technology, Madras. He did his post-doctoral research at the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada. Also, he is a Professor in the Department of Electrical Engineering at IIT Delhi.

He is presently the Chairman of the University Grants Commission and Professor of Electrical Engineering at IIT Delhi. In addition, he is the XII Vice-chancellor of Jawaharlal Nehru University, New Delhi (Jan 2016 – Feb 2022). He still teaches at IIT Delhi. Furthermore, he received the 2013 Award for Excellence in Teaching (in large class category) from IIT Delhi. “

Official UGC Website: https://www.ugc.ac.in/

For the complete UGC Notice detailing the news visit the link https://www.ugc.ac.in/pdfnews/3659158_Guildeline-for-engaing-Professor-of-Practice-in-Universities-and-Colleges.pdf

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The post is about the paper analysis of CSIR-UGC NET JUNE – 2022. It details the procedure to download the Question paper (Response Sheet) & the Answer key and then match the two to have an accurate estimate of your score.

The National Testing Agency has uploaded the Provisional Answer Keys, and Question Papers with Recorded Responses on the website https://csirnet.nta.nic.in/. The candidates, who are not satisfied with any Answer Key, may challenge the same by paying a fee of ₹200/- (Rupees Two Hundred only) per question challenged as a non-refundable processing fee.

The video alongside is a paper analysis video about CSIR-UGC NET JUNE – 2022. It details the procedure to download the Question paper (Response Sheet) & the Answer key and then match the two to have an accurate estimate for your score.

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Important Dates

Eligibility

• Criteria 1 :
  • Passed 10th class examination (under 10+2 system of education )
• Criteria 2 :
  • 8th Class passed
• Criteria 3 :
  • Passed 10th class examination (under 10+2 system of education with minimum of 40% independently in Science and Mathematics )

Important Links & Admission Procedure

• The candidates can register for online admission from any of the internet access points through the Website http://www.itidelhiadmissions.nic.in.
• Click on the ‘New Registration’ Link through the above link and fill the form in English.
• After generating registration number candidate needs to log in and select “FEE PAYMENT” link and pay the registration amount of ₹200 by any of the available modes.
• After paying the fee candidate needs to log in and click on “CHOICES” and select “FILL AND EDIT CHOICES”.
• After filling the choices as per their eligibility, the candidate must save the filled choices by Save Choice or Save & Exit button and take a print out of saved choices.
• Candidate can re-shuffle their Trade/ITI choices after registration and after each round of counseling, (if required) during specified time (20 – 22 June 2018)
• In Region, select:
  • Delhi, if you have passed your qualifying examination from a school located in Delhi
  • Outside Delhi if you have passed your qualifying examination from a school located outside Delhi
  • For NIOS students (National Institute of Open Schooling), the state of location of the study centre (school) will be considered as the state of the candidate.
•  The Candidate need to visit any Govt. ITI for the verification. Candidate should carry his original documents for verification along with a set of photo-copy(self attested) of all the relevant documents.
• Registration without verification is incomplete.
• Then a tentative rank listwould be prepared based on the marks of the candidate using the tie breaker criteria.
  • Tie Breaker Criteria: The rank of the candidate would be generated by calculating percentage of marks/grades secured by the candidate in qualifying examination and arranged in decreasing order. If two or more candidates are having same percentage/grade then, the following tie breaker criteria would be used in sequence to allot them distinctive ranks:-
    • Date of Birth: The candidate higher in age would be allotted the higher rank.
    • Science marks in descending order: If tie is still not broken then the candidate scoring higher marks in science would be allotted the higher rank.
    • Social Science: If tie is still not broken then the candidate scoring higher marks in social science would be allotted the higher rank.
    • Registration Number: if tie is still not broken then the candidate’s registration number in ascending order would be allotted the higher rank.
    • ( However, if still the tie does not break then CAO reserves the right to develop and implement further suitable criteria for distinguishing the rank of tied candidates. )
• If you find any discrepency in the rank, you should contact the II Help-desk. A Final rank listwould be displayed after incorporating the valid correction. Candidate must note his rank for future reference.
• Counseling Resultwould be publish on the online admission website.
• The allotted candidates should take a printout of his/her Allotment Letter by logging on the website and must report to the allotted ITI within specified time.
• If the candidate is satisfied with the allotted seat, he/she can opt for freezing his/her allotted seat by visiting the allotted ITI with all original certificates and photocopy of all relevant documents along with full course FEE.
• If the candidate wants to participate for higher preference seat in next counseling round, then he/she would have to visit the allotted ITI with copy of allotment letter and opt for the Up-Gradation. Upgraded candidate would be considered for next higher preference seat in the second round of counseling subject to availability of seats.
• Candidate would retain his/her previously allotted seat if new upgraded seat is not allotted to him during next counseling. However, If he/she is allotted a new seat as per his/her re-choice, then he/she will have no claim over his/her previously allotted seat. Retained /Upgraded candidates needs to compulsorily visit the ITI after every counseling for further Up-gradation/Freezing of seat otherwise his/her retained seat/newly allotted seat would get cancelled and candidate would not participate in next counseling round.
• In case NO SEAT is allotted, then the candidate will automatically participate in the next Round of Counseling.

Please  Note :

• Only one Registration form is to be filled to apply in different trades/ITIs. One mobile number can be used for only single registration.
• For more details about admission procedure visit, https://itidelhiadmissions.nic.in/publicinfo/Handler/FileHandler.ashx?i=File&ii=76&iii=Y
• All disputes will be subject to Delhi jurisdiction only.

Helpline Address

Link To Prospectus

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