Dr. Vikram Singh Mathematics, Engineering Mathematics, Ph.D
3 Reviews

Vikram Singh
Ph.D. Candidate in Mathematics
Mahendergarh District, Haryana, India.

Educational Background:

Doctor of Philosophy (Ph.D.):
Pursuing from Central University of Rajasthan, Kishangarh, Rajasthan, India.

Master of Science (Mathematics and Computing):
Indian Institute of Technology (IIT), Guwahati, Assam, India.

National-Level Qualifications:
CSIR NET-JRF (All India Rank 144)
GATE (2021 & 2022 Qualified)
IIT JAM (All India Rank 350)

Teaching Specialization:

I specialize in Mathematics and offer 1:1 personalized tutoring, both online and offline, focusing on deep conceptual understanding. My aim is to work with dedicated students who are eager to excel in competitive exams, including:
IIT-JEE
Mathematics Olympiad
Engineering Mathematics
I believe in a focused approach, mentoring students who truly wish to master mathematical concepts at a deeper level and crack challenging exams with confidence.

Subjects I Teach:
1. Linear & Abstract Algebra
• Linear Algebra:
Vector Spaces
Linear Transformations
Matrix Theory
Eigenvalues and Eigenvectors
Systems of Linear Equations
Determinants
Inner Product Spaces
Diagonalization
• Abstract Algebra:
Groups and Group Theory
Rings and Ring Theory
Fields and Field Theory
Modules and Vector Spaces
Homomorphisms and Isomorphisms
Polynomial Rings
Symmetry and Group Actions
2. Geometry
• Euclidean Geometry:
Points, Lines, and Planes
Angles and Triangles
Circles and Arcs
Polygons and Polyhedral
Conic Sections
• Non-Euclidean Geometry:
Hyperbolic Geometry
Elliptic Geometry
• Analytic Geometry:
Cartesian Coordinates
Distance and Midpoint Formulas
Equation of Lines and Planes
Conic Sections in the Plane
3. Trigonometry
• Basic Trigonometric Functions:
Sine, Cosine, Tangent
Reciprocal Functions: Cosecant, Secant, Cotangent
• Trigonometric Identities:
Pythagorean Identity
Angle Sum and Difference Formulas
Double Angle and Half Angle Formulas
Product-to-Sum and Sum-to-Product Formulas
•Inverse Trigonometric Functions
• Applications of Trigonometry:
Law of Sines and Law of Cosines
Trigonometric Equations
Polar Coordinates and Complex Numbers
4. Pre-calculus
• Algebraic Functions:
Polynomial Functions
Rational Functions
Exponential and Logarithmic Functions
• Trigonometric Functions:
Unit Circle
Graphs of Trigonometric Functions
Trigonometric Identities and Equations
•Sequences and Series:
Arithmetic Sequences
Geometric Sequences
Infinite Series and Convergence
• Conic Sections:
Parabolas, Ellipses, and Hyperbolas
5. Discrete Mathematics
• Set Theory:
Sets and Subsets
Venn Diagrams
Cartesian Products
• Logic and Propositional Calculus:
Boolean Algebra
Logical Operators and Truth Tables
Predicate Logic
• Combinatorics:
Permutations and Combinations
Pigeonhole Principle
Inclusion-Exclusion Principle
• Graph Theory:
Graphs and Subgraphs
Trees and Networks
Planar Graphs
Graph Coloring
6. Basic Mathematics
•Arithmetic:
Addition, Subtraction, Multiplication, Division
Fractions and Decimals
Ratios and Proportions
•Basic Algebra:
Linear Equations
Simple Inequalities
Polynomials
Factoring
• Geometry:
Basic Shapes and Properties
Perimeter, Area, and Volume
Angles and Triangles
• Number Systems:
Natural Numbers, Integers, Rational Numbers, Real Numbers
Prime Numbers and Factorization
7. Real & Complex Analysis
• Real Analysis:
Sequences and Series of Real Numbers
Continuity, Differentiability, and Integrability
Theorems: Bolzano-Weierstrass, Intermediate Value, Mean Value
Metric Spaces
• Complex Analysis:
Complex Numbers and Functions
Analytic Functions
Cauchy’s Theorem and Integral Formula
Laurent Series and Residues
Conformal Mapping
8. Numerical Analysis
• Numerical Solutions of Equations:
Bisection Method
Newton-Raphson Method
Fixed Point Iteration
• Interpolation and Extrapolation:
Polynomial Interpolation
Lagrange and Newton Interpolation
•Numerical Differentiation and Integration:
Trapezoidal Rule
Simpson’s Rule
Finite Difference Methods
• Numerical Linear Algebra:
Gauss Elimination
LU Decomposition
Eigenvalue Problems
• Error Analysis:
Truncation and Rounding Errors
Stability and Convergence
9. Calculus-1/2/3/4
• Calculus 1:
Limits and Continuity
Derivatives and Differentiation Techniques
Applications of Derivatives
Basic Integrals and Techniques of Integration
• Calculus 2:
Advanced Integration Techniques
Applications of Integrals
Sequences and Series
Parametric Equations and Polar Coordinates
• Calculus 3:
Multivariable Functions
Partial Derivatives
Multiple Integrals
Vector Calculus: Gradient, Divergence, Curl
• Calculus 4:
Advanced Topics in Vector Calculus
Green’s Theorem, Stokes’ Theorem, Divergence Theorem
Complex Integration
Fourier Series and Transforms
10. Ordinary & Partial Differential Equation
•Ordinary Differential Equations (ODEs):
First-Order Differential Equations
Second-Order Linear Equations
Systems of Linear Differential Equations
Series Solutions of ODEs
Laplace Transforms
•Partial Differential Equations (PDEs):
Classification of PDEs
Method of Separation of Variables
Fourier Series Solutions
Wave Equation, Heat Equation, Laplace’s Equation
Green’s Functions
11. Topology
•Basic Topological Concepts:
Open and Closed Sets
Basis for a Topology
Continuous Functions
Homeomorphisms
• Topological Spaces:
Compactness
Connectedness

12. Fourier Analysis
• Fourier Series:
Periodic Functions
Sine and Cosine Series
Convergence of Fourier Series

• Fourier Transforms:
Fourier Integral Theorem
• Applications:
Heat Equation
13. Number Theory
•Divisibility and Primes:
Greatest Common Divisor (GCD)
Fundamental Theorem of Arithmetic
Prime Number Theorem
•Congruences:
Modular Arithmetic
Chinese Remainder Theorem
Euler’s Theorem and Fermat’s Little Theorem

14. Laplace Transformation
• Laplace Transforms:
Definition and Basic Properties
Inverse Laplace Transform
Convolution Theorem
Application to Differential Equations
Laplace Transform of Special Functions
15.
• Differential Equations:
Advanced Techniques in PDEs
Numerical Methods for Differential Equations

16. Engineering Mathematics
• Linear Algebra and Matrix Theory:
Eigenvalues and Eigenvectors
Linear Systems and Stability
• Calculus and Differential Equations:
Differential Equations in Engineering
Fourier and Laplace Transforms
Complex Variables in Engineering

•Optimization:
Linear Programming
18. Applied Mathematics
• Mathematical Modelling:
Differential Equations in Applied Contexts
Optimization Problems
Mathematical modelling of control systems

• Statistics and Probability:
Probability Distributions
Statistical Inferences

19. Project Work:
Matlab
Mathematica
Maple

Current Role:
Ph.D. Candidate at Central University of Rajasthan, specializing in advanced mathematical topics and their applications.

Freelance Mathematics Tutor:
Providing personalized 1:1 tutoring and assignment help to students worldwide, ensuring they master subjects like Calculus, Linear Algebra, Differential Equations, and more.
Subject Matter Expert:
Actively working as an expert in Calculus, Advanced Mathematics, and Statistics & Probability with a proven track record of solving thousands of problems.

Specialty & Strengths:

Deep Conceptual Clarity:
I focus on breaking down complex mathematical concepts into easily understandable parts, ensuring a strong foundational understanding.

Exam-Oriented Preparation:
My teaching method is tailored to help students excel in competitive exams like IIT-JEE, Mathematics Olympiad, and Engineering Mathematics.

1:1 Focus:
I provide personalized attention to each student, understanding their unique learning needs and adjusting my teaching approach accordingly.
Expert Problem-Solver:
Having solved 12000+ problems on Chegg India, I bring strong problem-solving skills and practical applications to the table.

Researcher:
As a Ph.D. candidate in Mathematics, I stay updated with the latest advancements, and I incorporate this knowledge into my teaching to provide cutting-edge learning experiences.

Subjects

  • Discrete Mathematics Beginner-Expert

  • Numerical Analysis Beginner-Expert

  • Linear Algebra Beginner-Expert

  • Real Analysis Beginner-Expert

  • Probability and Random Process Expert

  • Linear Algebra (Engineering Level) Beginner-Expert

  • Differential Equations (Engineering Level) Diploma-Doctorate/PhD

  • Calculus 1, 2, 3, 4 Beginner-Expert

  • Differential Calculus Beginner-Expert

  • Mathematical Analysis Beginner-Expert

  • Engineering control systems Beginner-Expert

  • Statistics 1 Beginner-Expert

  • Mathematics (A level)

  • Discrete Math-288 Beginner-Expert

  • Multivariate and Vector Calculus Beginner-Expert

  • Differential Equations and Linear Algebra Beginner-Expert

  • Real and Complex Analysis Beginner-Expert

  • Multivariable and Vector Calculus Beginner-Expert

  • Linear Algebra (Advanced) Expert

  • Numerical Analysis for Engineering Beginner-Expert

Experience

  • Freelance (May, 2021–Present) at Online Teaching, India
    Tutoring 1:1 for students with class level -
    10th, 11th and 12th (Mathematics for NEET and JEE)
    - Engineering Mathematics
  • United States of America (Jun, 2020–Present) at Independent Online Tutor
  • India (Feb, 2019–Present) at 5 years experience as online chegg tutor
    I am working here as an subject matter expert in Calculus, Basic Math, Advanced Math and Statistics sice February 2019 . Till now i had solved around 4000 problems in mathematics on Chegg India.

Education

  • Ph.D (Oct, 2022–now) from Central University of rajasthan ajmer
  • CSIR NET JRF (Aug, 2021–Mar, 2022) from csir ugc net–scored AIR 144
  • Gate 2021 & 2022 (Mar, 2021–now) from IIT GATE
  • Mathematics and Computing (Jul, 2018–Jul, 2020) from INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI, GUWAHATI
  • B.Sc. (Jul, 2014–Jul, 2017) from UNIVERSITY OF RAJASTHAN JAIPUR

Fee details

    ₹1,200/hour (US$12.63/hour)

    I will charge minimum 1200 rupees for 1 hour.

Courses offered

  • Mathematics

    • US$20
    • Duration: 60 Hours
    • Delivery mode: Online
    • Group size: Individual
    • Instruction language: English, Hindi
    • Certificate provided: No
    I provide personalized 1:1 tutoring that emphasizes deep conceptual understanding and tailored strategies to help students excel in competitive exams like IIT-JEE, Mathematics Olympiad, and Engineering Mathematics.

  • Calculus 1,2,3,4

    • US$20
    • Duration: 60 Hours
    • Delivery mode: Online
    • Group size: Individual
    • Instruction language: English, Hindi
    • Certificate provided: No
    Calculus Teaching (1, 2, 3, 4):
    I provide comprehensive instruction in all levels of Calculus, from the basics to advanced concepts:

    Calculus 1:
    Focuses on the foundational topics of limits, continuity, derivatives, and the basics of integrals, preparing students to understand change and motion in mathematical terms.

    Calculus 2:
    Delves deeper into integration techniques, series and sequences, and introduces applications of integrals such as area, volume, and arc length.

    Calculus 3:
    Expands to multivariable calculus, covering partial derivatives, multiple integrals, vector calculus, and topics like gradient, divergence, and curl, essential for 3D analysis.

    Calculus 4:
    Engages with advanced topics such as differential equations, Green’s Theorem, Stokes’ Theorem, and complex integrals, with a focus on solving real-world mathematical problems.

    Through my teaching, I ensure students not only grasp the mechanics of each topic but also develop problem-solving skills applicable to real-world and academic challenges, preparing them for higher studies and competitive exams.

  • Ordinary and Partial Differential equation

    • US$20
    • Duration: 60 Hours
    • Delivery mode: Online
    • Group size: Individual
    • Instruction language: English, Hindi
    • Certificate provided: No
    I provide thorough instruction in Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), covering both fundamental principles and advanced problem-solving techniques:

    Ordinary Differential Equations (ODEs):
    I guide students through first-order and higher-order ODEs, systems of equations, and methods of solutions like separation of variables, integrating factors, and Laplace transforms. Real-world applications, such as modeling physical systems, are emphasized to solidify understanding.

    Partial Differential Equations (PDEs):
    For PDEs, I focus on solving equations involving functions of multiple variables, including topics like the heat equation, wave equation, and Laplace’s equation. Students learn methods like separation of variables, Fourier series, and numerical techniques, crucial for fields like physics, engineering, and applied mathematics.

    My approach helps students build a strong foundation in both theory and applications, preparing them for advanced studies, research, or tackling real-world problems involving differential equations.

  • Linear Algebra

    • US$20
    • Duration: 60 Hours
    • Delivery mode: Online
    • Group size: Individual
    • Instruction language: English, Hindi
    • Certificate provided: No
    Linear Algebra Teaching:

    I offer a structured and comprehensive approach to Linear Algebra, covering key concepts from the basics to advanced topics:

    Core Concepts:
    Students learn about vectors, matrices, determinants, and systems of linear equations, which form the foundation of linear transformations and vector spaces.
    Advanced Topics: I cover eigenvalues, eigenvectors, diagonalization, inner product spaces, and matrix factorizations (LU, QR, SVD), emphasizing their applications in solving real-world problems.

    Practical Applications:
    The focus extends to real-world use cases in areas like computer science, data analysis, machine learning, and physics, helping students understand how linear algebra is applied across various fields.
    My teaching ensures students not only master the computational techniques but also develop a deep conceptual understanding, preparing them for further studies and practical applications.

  • Complex Analysis

    • US$20
    • Duration: 60 Hours
    • Delivery mode: Online
    • Group size: Individual
    • Instruction language: English, Hindi
    • Certificate provided: No
    Complex Analysis Teaching:

    I provide an in-depth understanding of Complex Analysis, focusing on the study of functions of a complex variable:

    Fundamentals:
    Students are introduced to complex numbers, analytic functions, Cauchy-Riemann equations, and complex integration, laying the groundwork for more advanced concepts.

    Key Topics:
    I cover critical areas such as contour integration, Cauchy’s Integral Theorem and Formula, Taylor and Laurent series, residues, poles, and the application of residue theory to evaluate real integrals.

    Advanced Concepts:
    We explore conformal mappings, Mobius transformations, and their applications in fields such as fluid dynamics, electrostatics, and aerodynamics.

    Through my teaching, students gain a strong grasp of both the theoretical and practical aspects of complex analysis, preparing them for advanced research, engineering, and physical sciences applications.

  • Numerical Analysis

    • US$20
    • Duration: 60 Hours
    • Delivery mode: Online
    • Group size: Individual
    • Instruction language: English, Hindi
    • Certificate provided: No
    Numerical Analysis Teaching:

    I provide comprehensive instruction in Numerical Analysis, focusing on the development and application of numerical methods for solving mathematical problems:

    Core Topics:
    Students learn about root-finding algorithms (like bisection, Newton’s method), numerical integration and differentiation, interpolation, and polynomial approximation, which are essential for approximating solutions to complex problems.

    Linear Systems & Eigenvalue Problems:
    I cover numerical methods for solving systems of linear equations, such as Gaussian elimination and LU decomposition, as well as techniques for eigenvalue computation, including the power method and QR algorithm.

    Differential Equations:
    Emphasis is placed on numerical solutions to ordinary and partial differential equations using methods like Euler’s method, Runge-Kutta methods, and finite difference techniques for PDEs.

    Error Analysis:
    I teach students how to assess the accuracy and stability of numerical methods, ensuring a solid understanding of error propagation and convergence.

    By connecting theory with practical applications, I help students apply numerical techniques to real-world problems in engineering, science, and applied mathematics.

3 Reviews
5 out of 5

User Photo November 10, 2024
Payment verified US$ 10

Best Math Teacher On TeacherON

This guys is amazing and has a doctorate knowledge of mathematics. He is helping me in exam prep, Homework and other mathematics problems on PhD level. Thank you Vikram. I appreciate your help in this journey. Thanks again!!!

User Photo October 8, 2024
Payment verified US$ 11.77

Fantastic Tutor

Vikram is a great tutor, he has helped me learn and work on my math assignments in an extremely detailed manner. He ensures that I have all the right resources that I need to grasp the knowledge and I feel confident in what I work on. I received excellent scores on my assignments and he is a great tutor, thanks!

User Photo September 24, 2024
Payment verified US$ 10

Math Exams

I highly recommend this math tutor! His deep expertise truly shines through in every session, and his PhD-level knowledge is evident in the way he explains complex topics with ease. He is always punctual, professional, and well-prepared. Thanks to his guidance, I consistently scored 95% or higher on all my quizzes and exams. If you're looking for a dedicated and knowledgeable tutor, he's the best choice!

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