Lalit thuwal Higher Mathematics
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I am Lalit Thuwal, CSIR NET JRF RANK 4 (twice) and 9, NBHM, HRI, TIFR GS quallified, a Research scholor at IISC Bangalore.
In my classes, I ensure each topic is explained in simple and structured way so that students themself can think what should be done next in the proofs. I will help you to gain confidence, speed and accuracy.I am dedicated to making maths easy, logical and enjoyable for every learner. If you are preparing for any qualifiers in higher maths, I can help you with that also even if you love to spend time in mathematics you can contact me for further guidance.

I believe mathematics is not about memorizing formulas, but about understanding concepts and applying them smartly. My teaching method is designed to develop deep conceptual understanding, strong calculation skills, and a powerful problem-solving mindset. I myself has cleared all the competitive exams with single digit rank so I have that kind of experience of clearing exams. From basic foundations to advanced-level questions, I guide students with complete clarity. With personal attention, regular tests, and doubt-clearing sessions, I help students achieve their best performance.

If you have any doubts regarding the course you can ask me on whatsapp or email.

Subjects

Complex Analysis Beginner-Expert
Algebra 1, 2, 3 Beginner-Expert
Linear Algebra (Advanced) Beginner-Expert
Topology (General and Algebraic) Beginner-Expert
Real Analysis 1 & 2 Beginner-Expert

Experience

Faculty (Nov, 2020–Present) at Aing mathematics

My role includes right guidance in higher maths and prepare students for all competitive exams in higher maths.

Education

Research scholar (Aug, 2021–now) from IISC Bangalore

Fee details

₹40,000–100,000/week (US$421.01–1052.52/week)

Fees may vary depending on the subject and time requirements.

Courses offered

Ap calculus AB And BC
- ₹200000
- Duration: 2 Months
- Delivery mode: Online
- Group size: 5
- Instruction language: English, Hindi, Bengali
- Certificate provided: No
This course includes all calculus syllabus from basic to advance level. I can help you with your assignment problems and your doubts regarding the subjects. Students who are willing to learn how to think are most welcome. In this course I will guide you individually.
Functional Analysis
- ₹6000
- Duration: 2 Months
- Delivery mode: Online
- Group size: 5
- Instruction language: English, Hindi, Bengali
- Certificate provided: No
This course includes first course in functional analysis.
Galois theory
- ₹6000
- Duration: 2 Months
- Delivery mode: Online
- Group size: 5
- Instruction language: English, Hindi, Bengali
- Certificate provided: No
This course includes Field Extensions: Algebraic, normal, separable, and splitting fields.
Galois Theory Fundamentals: Galois groups, automorphism groups, and fixed fields.
Fundamental Theorem: The one-to-one correspondence between subfields and subgroups.
Applications: Solvability of polynomials by radicals, insolvability of the quintic, and cyclotomic extensions.
Structure: Finite fields and construction of Galois groups.
Algebra group and ring theory
- ₹5000
- Duration: 2 Months
- Delivery mode: Online
- Group size: 5
- Instruction language: English, Hindi
- Certificate provided: No
Fundamentals of Groups: Definition and examples (integer addition, modular arithmetic, symmetries of a square, permutation groups/symmetric groups dihedral groups,matrix groups).
Subgroups and Structure: Subgroup tests, cyclic groups and their subgroups, order of elements, centralizers, normalizers, and center of a group.
Permutations and Cosets: Cycle notation for permutations, even/odd permutations, alternating groups, cosets, and Lagrange's Theorem with consequences (e.g., Fermat’s Little Theorem).
Homomorphisms and Quotients: Normal subgroups, factor groups (quotient groups), group homomorphisms, isomorphism theorems, Cayley's theorem, automorphisms, and inner automorphisms.
Group Actions and Sylow Theorems: Group actions on sets, stabilizers, kernels, orbit-stabilizer theorem, Cauchy’s theorem, and Sylow’s theorems for finite groups.
Direct Products: External and internal direct products, and the Fundamental Theorem of Finite Abelian Groups.
Introduction to Rings: Definition, examples (integers, matrix rings, Gaussian integers), properties, and types of rings.
Subrings and Ideals: Subrings, ideals, operations on ideals, prime ideals, maximal ideals, and quotient/factor rings.
Ring Homomorphisms: Definitions, properties, kernel, and the three isomorphism theorems.
Integral Domains and Fields: Characteristics of a ring, integral domains, fields, and the field of quotients.
Polynomial Rings: Polynomial rings over commutative rings, division algorithm, factorization, and irreducibility tests (Eisenstein’s criterion).
Factorization Theory: Unique factorization domains (UFD), principal ideal domains (PID), and Euclidean domains.
Linear algebra
- ₹4000
- Duration: 2 Months
- Delivery mode: Online
- Group size: 5
- Instruction language: English, Hindi
- Certificate provided: No
Vector spaces: subspaces, sums and direct sums; Finite dimensional vector spaces: bases and dimensions; Linear maps: null-spaces and range, invertibility; Polynomials with real and complex coefficients; Eigenvalues and eigenvectors: triangularization and diagonalization of operators on finite dimensional vector spaces; Inner-product spaces: orthonormal bases, linear functional and adjoins; Operators on inner-product spaces: self-adjoint and normal operators, minimal polynomial, Jordan form; Traces and determinants of operators and matrices.
Analysis (Real, Complex)
- ₹8000
- Duration: 4 Months
- Delivery mode: Online
- Group size: 5
- Instruction language: English, Hindi
- Certificate provided: No
Real Analysis
Sequences and Series: Limits of sequences, convergence, Cauchy sequences, Bolzano-Weierstrass theorem, Limsup and Liminf, series convergence tests, absolute/conditional convergence.
Topology of the Real Line: Open and closed sets, limit points, interior points, boundary points, compactness (Heine-Borel theorem), connectedness.
Continuity and Limits of Functions: Limits of functions, continuity, types of discontinuity, uniform continuity,Intermediate Value Theorem, Extreme Value Theorem.
Differentiation: Derivatives, Mean Value Theorem, Rolle’s theorem, Taylor’s theorem, L'Hospital rules, monotone functions.
The Riemann Integral: Riemann sums, integrability conditions, Fundamental Theorem of Calculus, improper integrals.
Sequences and Series of Functions: Pointwise and uniform convergence, Weierstrass M-test, power series, radius of convergence, integration/differentiation of series.
Complex analysis
Complex numbers and elementary properties. Complex functions - limits, continuity and differentiation. Cauchy-Riemann equations. Analytic and harmonic functions. Elementary functions. Anti-derivatives and path (contour) integrals. Cauchy-Goursat Theorem. Cauchy's integral formula, Morera's Theorem. Liouville's Theorem, Fundamental Theorem of Algebra and Maximum Modulus Principle. Taylor series. Power series. Singularities and Laurent series. Cauchy's Residue Theorem and applications. Mobius transformations.
Topology
- ₹5000
- Duration: 2 Months
- Delivery mode: Online
- Group size: Individual
- Instruction language: English, Hindi
- Certificate provided: No
Fundamental Concepts: Definition of a topological space, basis and sub-basis, closed sets, closure, interior, limit points, and subspace topology.
Continuous Functions: Homeomorphisms, open and closed maps, and topological properties.
Connectedness: Connected spaces, path connectedness, components, and local connectedness.
Compactness: Compact spaces, Bolzano-Weierstrass property, limit point compactness, local compactness, and Tychonoff’s theorem.
Separation and Countability Axioms:
(Hausdorff), (regular)
(Normal) spaces; Urysohn's Lemma, Tietze extension theorem, and Urysohn's metrization theorem.
Product and Quotient Spaces: Product topology, projection maps, quotient topology.
Optional Topics: Nets and filters, Stone-Cech compactification.
PROBLEM SOLVING CLASSES (ISI, CMI, NBHM,TIFR level)
- ₹2000
- Duration: 1 Month
- Delivery mode: Online
- Group size: 5
- Instruction language: English, Hindi
- Certificate provided: No
In this course we solve good problems of different exams ISI,CMI, NBHM, TIFR. mainly focused on proof writing.