Calculus & Analytic Geometry(B.Sc 1st Semester, Core-I)

The 3.14 Class

Introduction to Algebra &amp; Number Theory

Algebra & Number Theory(B.Sc 1st Semester, Core-II)

Real Analysis - I (B.Sc 2nd Semester, Core-III)

Algebra - I (B.Sc 2nd Semester, Core-IV)

Probability (B.Sc 3rd Semester, Core-V)

Differential Equations - I (B.Sc 3rd Semester, Core-VI)

Linear  Algebra (B.Sc 3rd Semester, Core-VII)

Course Name: Real Analysis II 
Target Audience: B.Sc. Mathematics (Hons.) &ndash; 2nd Year, 4th Semester 
Course Validity: 6 Months 
Installment Plan: 3 Installments (each with 1-month validity access)
<h3>Course Description&nbsp;</h3>
<h3 style="text-align: justify;">&nbsp; &nbsp; &nbsp;This Real Analysis II course is a comprehensive and concept-driven program designed specifically for B.Sc. Mathematics (Hons.) 2nd Year, 4th Semester students. It systematically builds a deep understanding of advanced topics in real analysis, focusing on both theoretical rigor and problem-solving techniques essential for university examinations.</h3>
The course covers key areas such as differentiability, mean value theorems, Riemann integration, sequences and series of functions, uniform convergence, power series, and improper integrals. Special emphasis is placed on developing analytical thinking, proof-writing skills, and clarity of concepts.
In addition to university preparation, this course is highly beneficial for competitive examinations including CSIR-NET, GATE, JAM, and other entrance tests, where strong fundamentals in real analysis are crucial.
<h3>Key Features</h3>
<ul>
	<li style="text-align: left;">Conceptual clarity with step-by-step explanations</li>
	<li style="text-align: left;">Extensive problem-solving sessions and practice questions</li>
	<li style="text-align: left;">Focus on theorem understanding, proofs, and applications</li>
	<li style="text-align: left;">Exam-oriented preparation for semester exams and competitive tests</li>
	<li style="text-align: left;">Doubt-clearing support and guided learning approach</li>
</ul>
<h3>Course Structure</h3>
<ul>
	<li>Total Validity: 6 Months access to course content</li>
	<li>Flexible Payment Option: 3 Installments</li>
	<li>Each installment provides 1-month active access</li>
	<li>Well-structured modules aligned with university syllabus</li>
</ul>
<h3>Learning Outcomes</h3>
By the end of the course, students will be able to:
<ul>
	<li>Solve advanced problems involving derivatives and integrals</li>
	<li>Understand and apply convergence tests for sequences and series of functions</li>
	<li>Work confidently with Riemann and improper integrals</li>
	<li>Apply real analysis concepts in higher mathematics and competitive exams</li>
	<li>Develop strong proof-writing and analytical skills</li>
</ul>

Real Analysis - II(B.Sc 4th Semester, Core-VIII)

Multivariable Calculus(B.Sc 6th Semester, Core-XIV)

Core Paper - XIV,Model sate Modulo Syllabus For Under Graduate

<h2 style="text-align: center;">Course: Linear Algebra for CSIR-NET &amp; GATE (6-Month Validity)</h2>
This 6-month structured course is designed to provide a deep understanding of Linear Algebra, a crucial topic for CSIR-NET (Mathematical Sciences) and GATE (Mathematics &amp; Computer Science). The course covers essential theoretical concepts, problem-solving strategies, and exam-oriented techniques to help aspirants achieve a strong grasp of the subject.
<h3>Course Highlights:</h3>
✅ Vectors &amp; Matrices: Vector spaces, subspaces, basis, dimension, rank &amp; nullity 
✅ Linear Transformations: Kernel, image, matrix representation 
✅ Eigenvalues &amp; Eigenvectors: Diagonalization, Cayley-Hamilton theorem 
✅ Inner Product Spaces: Orthogonality, Gram-Schmidt process 
✅ Systems of Linear Equations: LU decomposition, consistency, and solutions 
✅ Special Matrices: Symmetric, Hermitian, unitary, and positive definite matrices 
✅ Exam-Focused Practice: Previous year questions, mock tests, and shortcuts
<h3>Course Benefits:</h3>
✔ Validity: Access for 6 months 
✔ Self-Paced Learning: Study at your convenience 
✔ Expert Guidance: Structured content aligned with CSIR-NET &amp; GATE syllabus 
✔ Comprehensive Practice: Solved examples and real exam-level questions
<h3>Who Should Enroll?</h3>
<ul>
	<li>CSIR-NET (Mathematical Sciences) aspirants</li>
	<li>GATE (Mathematics &amp; CS) candidates</li>
	<li>University students preparing for competitive exams</li>
</ul>
This course ensures a strong conceptual foundation and effective problem-solving skills, increasing your chances of success in CSIR-NET &amp; GATE.

<h2 style="text-align: center;">Course: Real Analysis for CSIR-NET &amp; GATE (6-Month Validity)</h2>
This 6-month structured course is designed to provide an in-depth understanding of Real Analysis, a crucial topic for CSIR-NET (Mathematical Sciences) and GATE (Mathematics). The course covers fundamental concepts, rigorous proofs, and problem-solving techniques, ensuring a strong foundation for competitive exams.
<h3>Course Highlights:</h3>
✅ Sequences &amp; Series: Convergence, Cauchy sequences, tests for series convergence 
✅ Continuity &amp; Differentiability: Uniform continuity, mean value theorems, Taylor series 
✅ Riemann &amp; Lebesgue Integration: Properties, improper integrals, fundamental theorems 
✅ Metric Spaces: Open &amp; closed sets, completeness, compactness, connectedness 
✅ Functions of Several Variables: Partial derivatives, Jacobians, extrema 
✅ Topology of Real Numbers: Limit points, Bolzano-Weierstrass theorem, Heine-Borel theorem 
✅ Exam-Oriented Problem Solving: Previous year questions, tricks, and strategies
<h3>Course Benefits:</h3>
<h3>✔ Validity: Access for 6 months 
✔ Self-Paced Learning: Study at your convenience 
✔ Expert Guidance: Structured content aligned with CSIR-NET &amp; GATE syllabus 
✔ Comprehensive Practice: Solved examples and real exam-level questions</h3>
<h3>Who Should Enroll?</h3>
<ul>
	<li>CSIR-NET (Mathematical Sciences) aspirants</li>
	<li>GATE (Mathematics) candidates</li>
	<li>University students preparing for competitive exams</li>
</ul>
By the end of the course, you&#39;ll gain a strong grasp of Real Analysis and enhance your problem-solving abilities to excel in CSIR-NET &amp; GATE.

Real Analysis CSIR NET & GATE Mathematics

<h3 style="text-align: center;">Course&nbsp;: Partial Differential Equations for CSIR NET &amp; GATE (6-Month Validity)</h3>
This 6-month comprehensive course on Partial Differential Equations (PDEs) is designed specifically for aspirants of CSIR NET (Mathematical Sciences) and GATE (Mathematics). The course aims to build a strong foundation in PDEs, covering both theoretical concepts and problem-solving techniques essential for cracking national-level competitive exams.
Starting from the fundamentals of PDEs, the course progresses through first-order and second-order equations, emphasizing classical equations like the Heat, Wave, and Laplace equations. It includes detailed lessons on method of characteristics, separation of variables, and transform methods (Laplace). Special focus is given to previous year questions, exam-specific tips, and short-cut methods.
The flexible 6-month access allows students to learn at their own pace while benefiting from regular doubt-clearing sessions, assignments, and practice tests modeled on CSIR NET and GATE patterns.
<h3>Key Highlights:</h3>
<ul>
	<li>
	6-month course access (self-paced + support)
	</li>
	<li>
	Covers entire PDE syllabus for CSIR NET &amp; GATE
	</li>
	<li>
	Video lectures, notes, and solved examples
	</li>
	<li>
	Topic-wise practice questions and mock tests
	</li>
	<li>
	Doubt-solving support via chat/email/live sessions
	</li>
	<li>
	Previous year question bank with detailed solutions
	</li>
</ul>
<h3>Topics Covered:</h3>
<ul>
	<li>
	Formation and classification of PDEs
	</li>
	<li>
	First-order PDEs and method of characteristics
	</li>
	<li>
	Second-order linear PDEs: Canonical forms, classification
	</li>
	<li>
	Classical PDEs:
	<ul>
		<li>
		Heat Equation
		</li>
		<li>
		Wave Equation
		</li>
		<li>
		Laplace Equation
		</li>
	</ul>
	</li>
	<li>
	Separation of variables
	</li>
	<li>
	Laplace transform techniques
	</li>
	<li>
	Boundary and initial value problems
	</li>
	<li>
	Application-oriented questions
	</li>
	<li>
	PYQ practice from CSIR NET and GATE
	</li>
</ul>
<h3>Who Should Enroll:</h3>
<ul>
	<li>
	CSIR NET Mathematical Sciences aspirants
	</li>
	<li>
	GATE Mathematics candidates
	</li>
	<li>
	MSc Mathematics/Physics/Engineering students preparing for exams or higher studies
	</li>
</ul>

Paid Courses

Calculus & Analytic Geometry(B.Sc 1st Semester, Core-I)

Algebra & Number Theory(B.Sc 1st Semester, Core-II)

Real Analysis - I (B.Sc 2nd Semester, Core-III)

Algebra - I (B.Sc 2nd Semester, Core-IV)

Probability (B.Sc 3rd Semester, Core-V)

Differential Equations - I (B.Sc 3rd Semester, Core-VI)

Linear Algebra (B.Sc 3rd Semester, Core-VII)

Real Analysis - II(B.Sc 4th Semester, Core-VIII)

Complex Analysis - I(B.Sc 4th Semester, Core-IX)

Algebra - II(B.Sc 4th Semester, Core-X)

Real Analysis - III(B.Sc 5th Semester, Core-XI)

Differential Equations - II(B.Sc 5th Semester, Core-XII)

Numerical Analysis & Scientific Computing(B.Sc 5th Semester, Core-XIII)

Multivariable Calculus(B.Sc 6th Semester, Core-XIV)

Differential Geometry(B.Sc 6th Semester, Core-XV)

Measure Theory & Integration(B.Sc 7th Semester, Core-XVI)

Algebra - III(B.Sc 7th Semester, Core-XVII)

Topology(B.Sc 7th Semester, Core-XVIII)

Mathematical Methods(B.Sc 7th Semester, Core-XIX)

Functional Analysis(B.Sc 8th Semester, Core-XX)

Analytic Number Theory(B.Sc 8th Semester, Core-XXI)

Complex Analysis - II(B.Sc 8th Semester, Core-XXII)

Differential Equations - III(B.Sc 8th Semester, Core-XXIII)

JAM Mathematics

Numerical Method & Scientific Computing

Group Theory - II

Linear Algebra CSIR NET & GATE Mathematics

Real Analysis CSIR NET & GATE Mathematics

PDE CSIR-NET GATE Mathematics

ALL

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