Your roadmap · आपका रोडमैप
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Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
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Semester 5 — subject classesसेमेस्टर 5 — विषयवार कक्षाएँEvery theory subject of the term, unit by unit, with notes, numericals and doubt classes.
Group and Ring Theory and Linear AlgebraNumber Theory and Game Theory
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Labs, practicals & project workलैब, प्रैक्टिकल और प्रोजेक्टExperiments / jobs / project work as in the syllabus, with practical file and viva preparation.
Mathematics Practical-V
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Unit tests & mid-termयूनिट टेस्ट और मिड-टर्मA test after every unit and a mid-term in the university / board pattern.
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Semester 5 mock testमॉक टेस्टA full mock test of all subjects before the exam, with analysis.
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Semester 5 exam (university / board)सेमेस्टर / वार्षिक परीक्षाPrevious papers, important questions and full revision.
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Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
सिलेबस · पाठ्यक्रम
3 subjects · 15 chapters · 74 topics
Group and Ring Theory and Linear Algebra6 chapters · 6 Months
Subject page →+
01Unit 1: Advanced Group Theory
5 टॉपिक+
- Automorphisms and inner automorphisms
- Conjugacy classes and class equation
- Cauchy's theorem
- Sylow theorems (statements and applications)
- Direct products
02Unit 2: Rings and Subrings
5 टॉपिक+
- Definition and examples of rings
- Integral domains and fields
- Zero divisors and units
- Characteristic of a ring
- Subrings
03Unit 3: Ideals and Ring Homomorphisms
5 टॉपिक+
- Ideals and quotient rings
- Prime and maximal ideals
- Ring homomorphisms and isomorphism theorems
- Polynomial rings
- Euclidean domains, PID and UFD (introduction)
04Unit 4: Vector Spaces
5 टॉपिक+
- Vector spaces and subspaces
- Linear span and linear independence
- Basis and dimension
- Sum and direct sum
- Quotient space
05Unit 5: Linear Transformations
6 टॉपिक+
- Linear transformations
- Kernel and range
- Rank-nullity theorem
- Matrix of a linear transformation
- Change of basis
- Eigenvalues and diagonalisation
06Unit 6: Inner Product Spaces
4 टॉपिक+
- Inner product and norm
- Cauchy-Schwarz inequality
- Orthogonality
- Gram-Schmidt orthogonalisation
Number Theory and Game Theory5 chapters · 6 Months
Subject page →+
01Unit 1: Divisibility
5 टॉपिक+
- Division algorithm
- GCD and the Euclidean algorithm
- LCM
- Primes and infinitude of primes
- Fundamental theorem of arithmetic
02Unit 2: Congruences
6 टॉपिक+
- Properties of congruences
- Linear congruences
- Chinese remainder theorem
- Fermat's little theorem
- Euler's theorem and phi function
- Wilson's theorem
03Unit 3: Diophantine Equations and Arithmetic Functions
5 टॉपिक+
- Linear Diophantine equations
- Pythagorean triples
- Number and sum of divisors
- Mobius function
- Perfect numbers
04Unit 4: Two-Person Zero-Sum Games
5 टॉपिक+
- Payoff matrix
- Maximin and minimax principle
- Saddle point and value of a game
- Pure strategies
- Fair games
05Unit 5: Mixed Strategies
5 टॉपिक+
- Games without saddle point
- Formula for 2 x 2 games
- Dominance principle
- Graphical method for 2 x n and m x 2 games
- Linear programming formulation of games
Mathematics Practical-V4 chapters · 6 Months
Subject page →+
01Groups and Rings on Computer
4 टॉपिक+
- Cayley tables and subgroups
- Units and zero divisors of Z_n
- Ideals of Z_n
- Checking Sylow counts for small groups
02Linear Algebra Computations
5 टॉपिक+
- Basis and dimension of a span
- Rank-nullity verification
- Matrix of a linear map
- Gram-Schmidt orthonormalisation
- Diagonalisation
03Number Theory Programs
5 टॉपिक+
- GCD and extended Euclidean algorithm
- Sieve of Eratosthenes
- Modular exponentiation and inverses
- Chinese remainder theorem
- Euler phi and divisor functions
04Game Theory
4 टॉपिक+
- Saddle point detection
- 2 x 2 mixed-strategy formula
- Dominance reduction
- Solving games by linear programming
About this course
आप यह कर पाएँगे
- Complete Group and Ring Theory and Linear Algebra syllabus with regular tests
- Complete Number Theory and Game Theory syllabus with regular tests
- Complete Mathematics Practical-V syllabus with regular tests
यह किसके लिए है
- B.Sc Mathematics students of Semester 5 (UP State Universities, NEP 2020)
- Students preparing for end-semester theory papers of Mathematics
आपको क्या चाहिए
- Algebra of Semester 3 (groups and homomorphisms)
- Matrices of Semester 2
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
सवाल
Which syllabus does this subject follow?
It follows the B.Sc Mathematics Semester 5 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.
How are students assessed at the centre?
Through unit-wise multiple-choice tests, a final test paper and doubt-clearing sessions that follow the university examination pattern.
Will this help in the semester examination?
Yes. Units are taught in the university order with solved numericals and exam-pattern questions.
Which syllabus does this lab course follow?
It follows the B.Sc Mathematics Semester 5 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.
