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Mathematics Practical-V (B.Sc Mathematics)

Computer exercises on algebraic structures, number theory and games.

6 महीनेअवधि 4Chapters18टॉपिक
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सिलेबस · पाठ्यक्रम

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01Groups and Rings on Computer 4 टॉपिक
  1. Cayley tables and subgroups
  2. Units and zero divisors of Z_n
  3. Ideals of Z_n
  4. Checking Sylow counts for small groups
02Linear Algebra Computations 5 टॉपिक
  1. Basis and dimension of a span
  2. Rank-nullity verification
  3. Matrix of a linear map
  4. Gram-Schmidt orthonormalisation
  5. Diagonalisation
03Number Theory Programs 5 टॉपिक
  1. GCD and extended Euclidean algorithm
  2. Sieve of Eratosthenes
  3. Modular exponentiation and inverses
  4. Chinese remainder theorem
  5. Euler phi and divisor functions
04Game Theory 4 टॉपिक
  1. Saddle point detection
  2. 2 x 2 mixed-strategy formula
  3. Dominance reduction
  4. Solving games by linear programming

परिचय

आप यह कर पाएँगे

  • Compute units, zero divisors and subgroups of Z_n on computer
  • Carry out linear algebra computations such as rank-nullity and Gram-Schmidt
  • Program the Euclidean algorithm, extended Euclid, sieve, modular powers and CRT
  • Detect saddle points and solve games by formula and linear programming

यह किसके लिए है

  • B.Sc Mathematics students of Semester 5 (UP State Universities, NEP 2020)
  • Students preparing for the B.Sc Mathematics practical examination and viva

आपको क्या चाहिए

  • Theory of Group and Ring Theory, Linear Algebra, Number Theory and Game Theory
  • Free mathematical software (Maxima / wxMaxima, SageMath or Python) installed

सवाल

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.

How are students assessed at the centre?

The trainer watches each experiment and marks it on a rubric (set-up, observations, calculation and viva); viva-style questions revise the theory behind the experiments.

Will this help in the semester examination?

Yes. The experiments match the university practical examination, including the record file and viva.

Download the syllabus (PDF)

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