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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Part 1 of the syllabusपाठ्यक्रम भाग 1Unit-wise coaching with notes and doubt classes.
Unit 1: Advanced Group TheoryUnit 2: Rings and SubringsUnit 3: Ideals and Ring Homomorphisms
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Part 2 of the syllabusपाठ्यक्रम भाग 2Unit-wise coaching with notes and doubt classes.
Unit 4: Vector SpacesUnit 5: Linear TransformationsUnit 6: Inner Product Spaces
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Unit tests & assignmentsयूनिट टेस्टRegular tests in the university / board pattern.
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Semester 5 exam (university / board)विश्वविद्यालय / बोर्ड परीक्षाPrevious papers and full revision before the exam.
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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
1 subject · 6 chapters · 30 topics
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
About this course
आप यह कर पाएँगे
- Use conjugacy, the class equation and Sylow theorems in finite groups
- Identify rings, integral domains and fields and their characteristic
- Work with ideals, quotient rings and ring homomorphisms
- Find bases and dimensions of vector spaces and subspaces
- Find kernel, range and matrices of linear transformations and apply rank-nullity
- Use inner products and the Gram-Schmidt process
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.
