Notes & SolutionsTMH-GRAPH-THEORY-VOLUME-I
Graph Theory — Volume I
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Graph Theory / Graph Algorithms / Discrete Graph TheoryUniversity / ADP, BS, legacy BSc, MSc and MS/MPhil foundation/revision
A 21-chapter university Graph Theory resource covering graph models, degree sequences, isomorphism, matrices, paths, connectivity, Eulerian and Hamiltonian graphs, trees, spanning trees, graph algorithms, planarity, duals, colouring, matching, digraphs, network flows, enumeration and applications.
8 mapped course placements
- ADP / Associate Degree Mathematics — Graph Theory / Introduction to Graph Theory discovery
- BS Mathematics — Graph Theory Volume I complete course resource
- Legacy BSc Mathematics — Graph Theory / Discrete Mathematics context
- MSc Mathematics — complete foundation and revision resource
- MS/MPhil Mathematics — foundation, prerequisite consolidation and revision; not a research-level replacement
- Mathematics Library — separate owner-resource record
- Graph Theory subject hub — one canonical child card
- Related from Discrete Mathematics, Linear Algebra, Numerical Analysis and Mathematics for Computing
Notes & SolutionsTMH-SPECIAL-FUNCTIONS-I
Special Functions-I — Volume I — Complete Solved Notes for BS & MSc Mathematics
Mehreen Kanwal — MPhil Mathematics · Rana Ali Hasan — MPhil Mathematics
Special Functions / Orthogonal Polynomials / Mathematical PhysicsUniversity / BS Mathematics, MSc Mathematics and legacy BSc/MSc revision
Study Special Functions I with solved BS/MSc notes on Gamma-Beta, hypergeometric, Bessel, Legendre, orthogonal polynomials, Airy functions and applications.
5 mapped course placements
- BS Mathematics — Books, Notes & Solutions → Special Functions / Mathematical Analysis / Mathematical Physics
- MSc Mathematics — Special Functions / Classical Special Functions revision and course discovery
- Legacy BSc/MSc Mathematics — Gamma/Beta, hypergeometric, Bessel, Legendre and orthogonal-polynomial revision
- Mathematics Library — separate owner-resource record
- Related from ODE, PDE, Complex Analysis, Real Analysis, Numerical Analysis, Linear Algebra and Mathematical Physics
Notes & SolutionsTMH-FUNCTIONAL-ANALYSIS-VOLUME-I
Functional Analysis I — Core Functional Analysis — Complete Course Book, Proofs & Solved Problems
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Functional Analysis / Operator TheoryBS Mathematics / Legacy MSc-BSc revision / MS-MPhil prerequisite and bridgeStudents moving from Real Analysis, Linear Algebra, Metric/Topology and Measure Theory into Functional AnalysisLearners who need theorem/proof structure plus solved exercises rather than a formula sheetInstructors or tutors looking for a chapter map and reference alignment, while using their own institutional syllabus as authoritySelf-learners preparing for advanced operator theory, PDE, harmonic analysis, variational methods or research-level coursework
Study Functional Analysis I (Core Functional Analysis) with chapter-wise definitions, theorems, proofs, solved work, university curriculum context, references and PDF access from The Math Hub. 36 chapters, Chapters 1–36 with chapter-wise definitions, theorem maps, proof scope, applications, crosswalks, references and dedicated FAQs.
6 mapped course placements
- BS Mathematics — Analysis / Functional Analysis discovery card
- Legacy BSc/MSc Mathematics — Functional Analysis revision where the approved scheme supports it
- MS/MPhil Mathematics — prerequisite, advanced theory or research-preparation discovery
- Functional Analysis subject hub — Volume child card
- Mathematics Library — separate owner-resource record
- Related from Real Analysis, Measure Theory, Topology, Linear Algebra, PDE and Approximation Theory
Notes & SolutionsTMH-FUNCTIONAL-ANALYSIS-VOLUME-II
Functional Analysis II — Advanced Functional Analysis — Complete Course Book, Proofs & Solved Problems
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Functional Analysis / Operator TheoryAdvanced BS Mathematics / MSc / MS-MPhil MathematicsStudents moving from Real Analysis, Linear Algebra, Metric/Topology and Measure Theory into Functional AnalysisLearners who need theorem/proof structure plus solved exercises rather than a formula sheetInstructors or tutors looking for a chapter map and reference alignment, while using their own institutional syllabus as authoritySelf-learners preparing for advanced operator theory, PDE, harmonic analysis, variational methods or research-level coursework
Study Functional Analysis II (Advanced Functional Analysis) with chapter-wise definitions, theorems, proofs, solved work, university curriculum context, references and PDF access from The Math Hub. 27 chapters, Chapters 37–63 with chapter-wise definitions, theorem maps, proof scope, applications, crosswalks, references and dedicated FAQs.
6 mapped course placements
- BS Mathematics — Analysis / Functional Analysis discovery card
- Legacy BSc/MSc Mathematics — Functional Analysis revision where the approved scheme supports it
- MS/MPhil Mathematics — prerequisite, advanced theory or research-preparation discovery
- Functional Analysis subject hub — Volume child card
- Mathematics Library — separate owner-resource record
- Related from Real Analysis, Measure Theory, Topology, Linear Algebra, PDE and Approximation Theory
Notes & SolutionsTMH-FUNCTIONAL-ANALYSIS-VOLUME-III
Functional Analysis III — Applications of Functional Analysis — Complete Course Book, Proofs & Solved Problems
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Functional Analysis / Operator TheoryAdvanced BS / MSc / MS-MPhil Mathematics; analysis and PDE applicationsStudents moving from Real Analysis, Linear Algebra, Metric/Topology and Measure Theory into Functional AnalysisLearners who need theorem/proof structure plus solved exercises rather than a formula sheetInstructors or tutors looking for a chapter map and reference alignment, while using their own institutional syllabus as authoritySelf-learners preparing for advanced operator theory, PDE, harmonic analysis, variational methods or research-level coursework
Study Functional Analysis III (Applications of Functional Analysis) with chapter-wise definitions, theorems, proofs, solved work, university curriculum context, references and PDF access from The Math Hub. 9 chapters, Chapters 64–72 with chapter-wise definitions, theorem maps, proof scope, applications, crosswalks, references and dedicated FAQs.
6 mapped course placements
- BS Mathematics — Analysis / Functional Analysis discovery card
- Legacy BSc/MSc Mathematics — Functional Analysis revision where the approved scheme supports it
- MS/MPhil Mathematics — prerequisite, advanced theory or research-preparation discovery
- Functional Analysis subject hub — Volume child card
- Mathematics Library — separate owner-resource record
- Related from Real Analysis, Measure Theory, Topology, Linear Algebra, PDE and Approximation Theory
Notes & SolutionsTMH-FUNCTIONAL-ANALYSIS-VOLUME-IV
Functional Analysis IV — Advanced Topics in Functional Analysis — Complete Course Book, Proofs & Solved Problems
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Functional Analysis / Operator TheoryMS-MPhil Mathematics / advanced MSc / research-preparation readingStudents moving from Real Analysis, Linear Algebra, Metric/Topology and Measure Theory into Functional AnalysisLearners who need theorem/proof structure plus solved exercises rather than a formula sheetInstructors or tutors looking for a chapter map and reference alignment, while using their own institutional syllabus as authoritySelf-learners preparing for advanced operator theory, PDE, harmonic analysis, variational methods or research-level coursework
Study Functional Analysis IV (Advanced Topics in Functional Analysis) with chapter-wise definitions, theorems, proofs, solved work, university curriculum context, references and PDF access from The Math Hub. 12 chapters, Chapters 73–84 with chapter-wise definitions, theorem maps, proof scope, applications, crosswalks, references and dedicated FAQs.
6 mapped course placements
- BS Mathematics — Analysis / Functional Analysis discovery card
- Legacy BSc/MSc Mathematics — Functional Analysis revision where the approved scheme supports it
- MS/MPhil Mathematics — prerequisite, advanced theory or research-preparation discovery
- Functional Analysis subject hub — Volume child card
- Mathematics Library — separate owner-resource record
- Related from Real Analysis, Measure Theory, Topology, Linear Algebra, PDE and Approximation Theory
Notes & SolutionsTMH-LA-COMPLETE-BOOK
Linear Algebra — Complete Course Book, Theorems, Proofs & Solved Problems
Rana Ali Hasan · Mehreen Kanwal
Linear AlgebraUniversity / Undergraduate
19-chapter Linear Algebra resource with matrices, systems, vector spaces, transformations, eigenvalues, orthogonality, spectral theory, canonical forms and computational applications.
6 mapped course placements
- ADP Mathematics — Books, Notes & Solutions → Algebra / Linear Algebra
- BS Mathematics — Books, Notes & Solutions → Algebra / Linear Algebra
- Legacy BSc Mathematics — Books, Notes & Solutions → Algebra / Linear Algebra
- Mathematics Library — separate owner-resource record
- Algebra subject hub — Linear Algebra child card
- Mathematics for Computing & Other Programs — contextual Linear Algebra discovery
Notes & SolutionsTMH-AA1-GROUP-THEORY
Abstract Algebra-I (Algebra-I / Algebra 1): Group Theory — Complete Course Book
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Group TheoryUniversity / Undergraduate
18-chapter proof-based Group Theory resource covering algebraic preliminaries, groups, subgroups, cyclic groups, cosets, homomorphisms, actions, Cauchy and Sylow theory.
6 mapped course placements
- ADP Mathematics — Books, Notes & Solutions → Algebra (where Group Theory is offered)
- BS Mathematics — Books, Notes & Solutions → Algebra / Abstract Algebra
- Legacy BSc Mathematics — Books, Notes & Solutions → Algebra
- Mathematics Library — separate owner-resource record
- Abstract Algebra hub — Algebra-I / Group Theory child card
- Related from Linear Algebra — separate algebra-family resource
Notes & SolutionsTMH-ODE-COMPLETE-BOOK
Ordinary Differential Equations (ODE) — Complete Course Notes & Book
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Ordinary Differential Equations (ODE)University / ADP, BS, BSc and MSc revision
Study Ordinary Differential Equations (ODE) with first-order methods, Laplace transforms, systems, series, Sturm–Liouville, numerical methods and applications. 26 visible chapters progress from first-order equations to dynamical systems, Sturm–Liouville theory, numerical methods and asymptotics.
7 mapped course placements
- ADP Mathematics — Books, Notes & Solutions → Differential Equations / Applied Mathematics
- BS Mathematics — Books, Notes & Solutions → Differential Equations / Applied Mathematics
- Legacy BSc Mathematics — Books, Notes & Solutions → Differential Equations
- Legacy MSc Mathematics — Books, Notes & Solutions → Differential Equations / Mathematical Methods
- Mathematics Library — separate owner-resource record
- Mathematics for Computing & Other Programs — contextual ODE discovery where relevant
- Related from Numerical Analysis, PDE, Mathematical Modelling, Calculus and Linear Algebra
Notes & SolutionsTMH-NUMERICAL-ANALYSIS-I
Numerical Analysis-I / Numerical Methods — Complete Course Book
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Numerical Analysis / Numerical MethodsUniversity / ADP, BS, BSc, MSc and Computing
Study Numerical Analysis-I / Numerical Methods in a 40-chapter Math Hub course book with 293 worked examples covering errors, roots, linear systems, interpolation, ODEs, PDEs, FEM, optimization and FFT.
7 mapped course placements
- BS Mathematics — Books, Notes & Solutions → Numerical Analysis / Numerical Methods
- ADP / Associate Degree Mathematics — relevant Numerical Methods discovery
- Legacy BSc/MSc Mathematics — Numerical Analysis / Numerical Methods revision
- Mathematics for Computing & Other Programs — contextual numerical-computing discovery
- Mathematics Library — separate owner-resource record
- Numerical Analysis subject hub — one canonical child resource
- Related from Linear Algebra, ODE, PDE, Calculus and Mathematical Computing
Notes & SolutionsTMH-THEORY-OF-SPLINES-VOLUME-II
Theory of Splines — Volume II
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Theory of Splines-II / Bézier Curves / B-Splines / Cubic Splines / ApproximationUniversity / BSc, BS and MSc Mathematics
Bézier Curves · B-Splines · Cubic Splines · 16 Chapters · Solved Exercises
6 mapped course placements
- BS Mathematics — Theory of Splines-II / Theory of Approximation and Splines-II
- BSc Mathematics — advanced approximation, geometric modelling and spline revision
- MSc Mathematics — spline functions, approximation and computational mathematics context
- Mathematics Library — canonical Volume II resource record
- Spline subject hub — Spline → Spline II → one canonical detail page
- Related from Volume I, Numerical Analysis, Linear Algebra, Differential Geometry and CAGD
Notes & SolutionsTMH-NUMERICAL-ANALYSIS-II
Numerical Analysis-II / Numerical Methods-II — Advanced Numerical Methods & Scientific Computing
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Numerical Analysis-II / Numerical Methods-IIUniversity / BS, MSc, MS/MPhil and scientific computing
Study Numerical Analysis II / Numerical Methods II with 40 detailed chapters on quadrature, ODEs, stability, BVPs, Krylov methods, PDEs, FEM, optimization and scientific computing. View or download the complete Math Hub book.
7 mapped course placements
- BS Mathematics — Books, Notes & Solutions → Numerical Analysis / Numerical Methods
- ADP Mathematics — only where the current programme mapping includes a second or advanced numerical-methods course
- Legacy BSc/MSc Mathematics — Numerical Analysis / Numerical Methods revision
- Mathematics Library — separate owner-resource discovery card
- Numerical Analysis subject hub — one Numerical Analysis-II child card
- Mathematics for Computing & Other Programs — contextual Scientific Computing / Numerical Methods discovery
- Related from Numerical Analysis-I, ODE, PDE, Linear Algebra and Vector & Tensor Analysis
BooksLIB-0008
A First Course in Linear Algebra
Robert A. Beezer
AlgebraBS
Author / University of Puget Sound · Version 3.50 (2015) · GNU Free Documentation License
BooksLIB-0649
A First Course in Linear Algebra - 10th Edition-2023-B-D
Ken Kuttler
AlgebraADP / BS / MS-MPhil
Lyryx · 2023 · Attribution
BooksLIB-0066
An Introductory Course in Linear Algebra
Khalid Latif Mir
AlgebraADP / BS
Ilmi Kitab Khana · Various editions · Commercial copyright
BooksLIB-0088
Applied Linear Algebra in Action
Katsikis, Vasilios N.
AlgebraADP / BS / MS-MPhil
IntechOpen · 2016 · https://creativecommons.org/licenses/by/3.0/
BooksLIB-0276
Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
Stephen Boyd; Lieven Vandenberghe
AlgebraBS / MS-MPhil
Cambridge University Press · 2018 · Copyright CUP; web copy authorized by publisher
BooksLIB-0687
Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students
Jason Lachniet
AlgebraADP / BS / MS-MPhil
Jason Lachniet · 2017 · Attribution-ShareAlike
BooksLIB-0298
Linear Algebra
Abid Yasser, Hassan
AlgebraADP / BS / MS-MPhil
IntechOpen · 2012 · https://creativecommons.org/licenses/by/3.0/
BooksLIB-0645
Linear Algebra
David Cherney
AlgebraADP / BS / MS-MPhil
University of California, Davis · 2016 · Attribution-NonCommercial-ShareAlike
BooksLIB-0299
Linear Algebra
Jim Hefferon
AlgebraBS
Author / OpenIntro distribution · Current free edition · Free/open materials; see author license page
BooksLIB-0301
Linear Algebra. A Course for Physicists and Engineers
Haubold, Hans J.; Mathai, Arak M.
AlgebraADP / BS / MS-MPhil
De Gruyter · 2017 · https://creativecommons.org/licenses/by-nc-nd/4.0/
BooksLIB-0302
Linear Algebra Done Right
Axler, Sheldon
AlgebraADP / BS / MS-MPhil
Springer Nature · 2024 · https://creativecommons.org/licenses/by-nc/4.0/
BooksLIB-0303
Linear Algebra Done Wrong
Sergei Treil
AlgebraBS
Author · Current open edition · CC BY-NC-ND
BooksLIB-0648
Linear Algebra, Theory And Applications
Kenneth Kuttler
AlgebraADP / BS / MS-MPhil
Saylor Foundation · 2012 · Attribution-ShareAlike
BooksLIB-0685
Linear Algebra with Applications - 2023-A-D
W. Keith Nicholson
AlgebraADP / BS / MS-MPhil
Lyryx · 2023 · Attribution-NonCommercial-ShareAlike
BooksLIB-0432
Numerical Linear Algebra and the Applications
Jbilou, Khalide; Mitrouli, Marilena
AlgebraADP / BS / MS-MPhil
MDPI - Multidisciplinary Digital Publishing Institute · 2021 · https://creativecommons.org/licenses/by/4.0/
BooksLIB-0726
Tea Time Linear Algebra Explorations in Mathematics - 2nd Edition
Leon Q. Brin
AlgebraADP / BS / MS-MPhil
Leon Q. Brin · 2022 · Attribution-ShareAlike
BooksLIB-0618
Understanding Linear Algebra
David Austin
AlgebraBS
Grand Valley State University / Author · Current open edition · Creative Commons Attribution
BooksLIB-0300
Linear Algebra
Mathai, Arak M.; Haubold, Hans J.
CalculusADP / BS / MS-MPhil
De Gruyter · 2017 · https://creativecommons.org/licenses/by-nc-nd/4.0/
