Develops quantitative mean-value and omega-result techniques for the zeta function. A research continuation rather than a first introduction to primes.
K. Ramachandra · Long lecture notes · Research · English
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Develops quantitative mean-value and omega-result techniques for the zeta function. A research continuation rather than a first introduction to primes.
Preparation: Analytic number theory; zeta functions; complex-variable estimates.
Version: TIFR Lectures on Mathematics 85; authorized retypeset historical edition — original date on title page · Checked 2026-10-11
Develops analytic properties of the zeta function. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
K. Chandrasekharan · Long lecture notes · Graduate · English
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Develops analytic properties of the zeta function. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Preparation: Complex analysis; elementary number theory.
Use: Bridge toward analytic number theory.
Version: TIFR volume 1; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11
Carl Ludwig Siegel · Long lecture notes · Research · English
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A specialized course in celestial-mechanics dynamics and singularity analysis. This is a research branch, not a first qualitative ODE course.
Preparation: ODE, mechanics, complex analysis and dynamical systems.
Version: TIFR Lectures on Mathematics 42; authorized retypeset historical edition — original date on title page · Checked 2026-10-11
Studies surgery-theoretic and topological manifold results. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Michel A. Kervaire · Long lecture notes · Graduate · English
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Studies surgery-theoretic and topological manifold results. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
A classical algebraic-function course at the interface with Riemann surfaces. Algebraic viewpoint and historical notation differ from a first contour-integral course.
Max Deuring · Long lecture notes · Graduate · English
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A classical algebraic-function course at the interface with Riemann surfaces. Algebraic viewpoint and historical notation differ from a first contour-integral course.
Preparation: Complex analysis; field extensions; curves.
Version: TIFR Lectures on Mathematics 18; authorized retypeset historical edition — original date on title page · Checked 2026-10-11
Develops analytic methods in several complex variables. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Bernard Malgrange · Long lecture notes · Graduate · English
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Develops analytic methods in several complex variables. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Preparation: Complex analysis; sheaf language.
Use: Bridge into complex analytic geometry.
Version: TIFR volume 13; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11
Philippe G. Ciarlet · Long lecture notes · Research · English
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A mathematical-elasticity course linking PDE and continuum models. Applied orientation is explicit; it is not a general first PDE course.
A classical route to algebraic K-theory from rings and projective modules. Compare with modern higher-K-theory references before using later categorical constructions.
Hyman Bass · Long lecture notes · Research · English
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A classical route to algebraic K-theory from rings and projective modules. Compare with modern higher-K-theory references before using later categorical constructions.
A focused treatment of mean-periodic phenomena and uniqueness. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Jean Delsarte · Long lecture notes · Graduate · English
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A focused treatment of mean-periodic phenomena and uniqueness. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Preparation: Fourier analysis; distributions.
Use: Further harmonic-analysis study.
Version: TIFR volume 22; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11
Patrick J. Rabier · Long lecture notes · Research · English
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A specialist course on how solutions change with a parameter. Functional-analytic preparation is needed beyond an elementary phase-plane course.
A focused introduction to analytical aspects of stochastic equations. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Daniel W. Stroock · Long lecture notes · Graduate · English
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A focused introduction to analytical aspects of stochastic equations. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
Preparation: Probability; stochastic calculus.
Use: Advanced stochastic-analysis course.
Version: TIFR volume 68; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11
A toric-geometry bridge connecting combinatorial cones and algebraic-geometric constructions. It complements, rather than replaces, a differential-geometric manifold course.
Tadao Oda · Long lecture notes · Research · English
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A toric-geometry bridge connecting combinatorial cones and algebraic-geometric constructions. It complements, rather than replaces, a differential-geometric manifold course.
Preparation: Algebraic geometry; lattices and convex cones.
Version: TIFR Lectures on Mathematics 58; authorized retypeset historical edition — original date on title page · Checked 2026-10-11
A focused study of factorization and commutative-ring structure. Useful for clarifying the distinction between elements, ideals and divisor-theoretic methods.
Pierre Samuel · Long lecture notes · Graduate · English
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A focused study of factorization and commutative-ring structure. Useful for clarifying the distinction between elements, ideals and divisor-theoretic methods.
Preparation: Commutative algebra; integral domains.
Version: TIFR Lectures on Mathematics 30; authorized retypeset historical edition — original date on title page · Checked 2026-10-11
Develops mathematical methods for propagating waves. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
G. B. Whitham · Long lecture notes · Graduate · English
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Develops mathematical methods for propagating waves. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.
A graduate course connecting Lie groups, Lie algebras and representations. Initial manifold material helps orientation but does not remove the need for mathematical maturity.
Pavel Etingof · Course notes · Intermediate · English (legacy metadata)
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A graduate course connecting Lie groups, Lie algebras and representations. Initial manifold material helps orientation but does not remove the need for mathematical maturity.
Preparation: Abstract algebra; topology and smooth manifolds.
Balances Gaussian elimination with vector spaces and proofs. Worked solutions to all exercises are useful for independent study; suitable before an operator-focused second course.
Jim Hefferon · Textbook · Introductory · English (legacy metadata)
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Balances Gaussian elimination with vector spaces and proofs. Worked solutions to all exercises are useful for independent study; suitable before an operator-focused second course.
A proof-based, operator-centered second course that introduces determinants late. Especially useful for structural understanding; not designed primarily as a computational matrix handbook.
Sheldon Axler · Textbook · Intermediate · English (legacy metadata)
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A proof-based, operator-centered second course that introduces determinants late. Especially useful for structural understanding; not designed primarily as a computational matrix handbook.
Develops vector spaces, matrices, determinants, eigenvalues and inner products, followed by tensor constructions, differential equations and matrix groups. The author identifies Chapters 1–5 as the required core; later…
李思 (Si Li) · Course notes · Introductory · Chinese
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Public full text; checked against the title and contents.已核对题名和目录，可公开阅读全文。
Original title: 线性代数
Develops vector spaces, matrices, determinants, eigenvalues and inner products, followed by tensor constructions, differential equations and matrix groups. The author identifies Chapters 1–5 as the required core; later chapters are optional.先讲向量空间、矩阵、行列式、特征值和内积，再讨论张量构造、微分方程与矩阵群。作者将前五章列为必修主线，后续章节可选读。
Preparation: School algebra and elementary functions.中学代数与初等函数。
Use: Use Chapters 1–5 for a first course; choose later applications after that foundation.第一遍以第1—5章为主，建立基础后再选读应用部分。