Your roadmap · आपका रोडमैप
- 1
Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
- 2
Semester 3 — subject classesसेमेस्टर 3 — विषयवार कक्षाएँEvery theory subject of the term, unit by unit, with notes, numericals and doubt classes.
Algebra and Mathematical Methods
- 3
Labs, practicals & project workलैब, प्रैक्टिकल और प्रोजेक्टExperiments / jobs / project work as in the syllabus, with practical file and viva preparation.
Mathematics Practical-III
- 4
Unit tests & mid-termयूनिट टेस्ट और मिड-टर्मA test after every unit and a mid-term in the university / board pattern.
- 5
Semester 3 mock testमॉक टेस्टA full mock test of all subjects before the exam, with analysis.
- 6
Semester 3 exam (university / board)सेमेस्टर / वार्षिक परीक्षाPrevious papers, important questions and full revision.
- 7
Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
Syllabus · पाठ्यक्रम
2 subjects · 9 chapters · 45 topics
Algebra and Mathematical Methods5 chapters · 6 Months
Subject page →+
01Unit 1: Groups
6 topics+
- Binary operations
- Definition and examples of groups
- Abelian groups and order of an element
- Subgroups
- Cyclic groups
- Cosets and Lagrange's theorem
02Unit 2: Normal Subgroups and Homomorphisms
6 topics+
- Normal subgroups
- Quotient groups
- Homomorphism and kernel
- Isomorphism theorems
- Permutation groups
- Cayley's theorem
03Unit 3: Laplace Transforms
6 topics+
- Definition and existence
- Linearity and shifting theorems
- Transforms of derivatives and integrals
- Inverse Laplace transform
- Convolution theorem
- Solving linear ODEs
04Unit 4: Fourier Series and Transforms
5 topics+
- Fourier series and Dirichlet conditions
- Even and odd functions
- Half-range series
- Fourier transform
- Fourier sine and cosine transforms
05Unit 5: Special Functions
5 topics+
- Legendre equation and polynomials
- Rodrigues' formula and generating function
- Orthogonality of Legendre polynomials
- Bessel equation and Bessel functions
- Recurrence relations
Mathematics Practical-III4 chapters · 6 Months
Subject page →+
01Group Theory on Computer
5 topics+
- Cayley tables of Z_n and U(n)
- Checking group axioms
- Orders of elements
- Cyclic subgroups and cosets
- Permutation groups
02Laplace Transforms
4 topics+
- laplace() and ilt() commands
- Shifting theorems checked on computer
- Solving IVPs with Laplace transforms
- Convolution
03Fourier Series and Transforms
4 topics+
- Computing Fourier coefficients
- Plotting partial sums
- Gibbs phenomenon
- Half-range series
04Special Functions
4 topics+
- Legendre polynomials (legendre_p)
- Verifying orthogonality
- Bessel functions (bessel_j) and their plots
- Checking recurrence relations
About this course
You will be able to
- Complete Algebra and Mathematical Methods syllabus with regular tests
- Complete Mathematics Practical-III syllabus with regular tests
Who it is for
- B.Sc Mathematics students of Semester 3 (UP State Universities, NEP 2020)
- Students preparing for end-semester theory papers of Mathematics
What you need
- Mathematics of Semesters 1 and 2
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
Questions
Which syllabus does this subject follow?
It follows the B.Sc Mathematics Semester 3 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 3 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.
