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-COMPETITIVE-BASIC-MATH-14
Algebraic Expressions, Identities & Factorization MCQs — 100 Solved Questions
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Algebraic Expressions, Identities & Factorization MCQsCompetitive Exams / PPSC, FPSC & One-Paper Preparation
100 fully solved questions covering terms/coefficient/substitution, like terms, algebraic simplification, expansion of brackets, standard identities, difference of squares. Every MCQ includes four options and immediate mathematical working for fast competitive-exam practice.
3 mapped course placements
- Competitive Exams → Basic Math MCQs / One-Paper pathway
- Mathematics Library → Notes & Solutions → Solved MCQ Booklet
- PPSC, FPSC, CSS MPT, PMS and NTS → verify current official notice before use
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-TOPOLOGY-VOLUME-I
Topology — Volume I: General Topology / Point-Set Topology — Complete Course Book
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Topology / General Topology / Point-Set TopologyUniversity / ADP, BS, BSc and MSc revision
Study Topology from metric spaces and topological spaces to continuity, compactness, connectedness, separation, metrization, nets, filters, Tychonoff theory and advanced General Topology with proofs, examples and exercises. 45 chapters, 305 A4 pages, 414 theorem/result boxes, 133 formal definition boxes, 56 worked examples and 170 topic-wise unsolved exercises.
7 mapped course placements
- ADP / Associate Degree Mathematics — relevant where Basic Topology or Metric & Topological Spaces is offered
- BS Mathematics — Topology / General Topology / Point-Set Topology
- Legacy BSc Mathematics — Set Topology and Metric Spaces revision
- MSc Mathematics — General Topology foundation and revision context
- Mathematics Library — separate owner-resource record
- Topology subject hub — Volume I child card
- Related from Real Analysis, Metric Spaces, Functional Analysis, Differential Geometry, Manifolds and Algebraic Topology
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-AA2-RINGS-FIELDS-MODULES
Abstract Algebra-II (Algebra-II / Algebra 2): Rings, Fields & Modules — Complete Course Book
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Rings, Fields & ModulesUniversity / Undergraduate and revision
23-chapter Abstract Algebra-II resource covering rings, ideals, quotient rings, ED/PID/UFD, polynomial rings, finite fields, extensions and modules.
6 mapped course placements
- ADP Mathematics — Books, Notes & Solutions → Algebra (where Rings, Fields & Modules is offered)
- BS Mathematics — Books, Notes & Solutions → Algebra / Abstract Algebra
- Legacy BSc/MSc Mathematics — Algebra resources
- Mathematics Library — separate owner-resource record
- Abstract Algebra hub — Algebra-II / Rings, Fields & Modules child card
- Related from Abstract Algebra-I — continuation resource
Notes & SolutionsTMH-NUMBER-THEORY
Number Theory — Complete Course Notes & Book
Mehreen Kanwal — MPhil Mathematics · Rana Ali Hasan — MPhil Mathematics
Number TheoryUniversity / Undergraduate and advanced bridge
Study Number Theory from divisibility and primes to congruences, quadratic reciprocity, Diophantine equations, continued fractions, algebraic number theory, finite fields and cryptographic applications, with proofs, worked examples and exercises.
8 mapped course placements
- ADP / Associate Degree Mathematics — Books, Notes & Solutions → Number Theory / Pure Mathematics
- BS Mathematics — Books, Notes & Solutions → Number Theory / Pure Mathematics
- Legacy BSc Mathematics — Books, Notes & Solutions → Number Theory / Higher Arithmetic
- Legacy MSc / revision — foundation discovery where Number Theory is relevant
- Mathematics Library — separate owner-resource record
- University Mathematics / Pure Mathematics subject hub — Number Theory child card
- Mathematics for Computing & Other Programs — contextual discovery from Discrete Mathematics, Cryptography and Finite Fields
- Related from Discrete Mathematics, Abstract Algebra and Cryptography — one canonical Number Theory page
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-0006
A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation
Groh, Dennis
AlgebraBS / MS-MPhil / PhD
Logos Verlag Berlin · 2024 · https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
BooksLIB-0786
A First Book in Algebra
Boyden, Wallace C. (Wallace Clarke), 1858-1937
AlgebraADP / BS / MS-MPhil
Project Gutenberg · Project Gutenberg public-domain/free-ebook access; check local jurisdiction where applicable.
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-0781
A Primer of Quaternions
Hathaway, Arthur S. (Arthur Stafford), 1855-1934
AlgebraADP / BS / MS-MPhil
Project Gutenberg · Project Gutenberg public-domain/free-ebook access; check local jurisdiction where applicable.
BooksLIB-0872
A Review of Algebra
Rivenburg, Romeyn Henry
AlgebraADP / BS / MS-MPhil
Project Gutenberg · Project Gutenberg public-domain/free-ebook access; check local jurisdiction where applicable.
BooksLIB-0012
Abstract Algebra: Theory and Applications
Thomas W. Judson
AlgebraBS / MS-MPhil
Judson Books / Orthogonal print edition · 2025 edition; current PDF updated Aug 11, 2026 · Open-source licensing; see official page
BooksLIB-0730
Advanced Algebra v. 1.0
John Redden
AlgebraADP / BS / MS-MPhil
2012 · Attribution-NonCommercial-ShareAlike
BooksLIB-0054
Algebra: Abstract and Concrete
Frederick M. Goodman
AlgebraBS / MS-MPhil
Author / University of Iowa · Edition 2.6 (2014) · Copyright author; official free download
BooksLIB-0653
Algebra and Trigonometry 2e
Jay Abramson
AlgebraADP / BS / MS-MPhil
OpenStax · 2021 · Attribution
BooksLIB-0055
Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique
Jens Høyrup
AlgebraADP / BS / MS-MPhil
Edition Open Access · 2017 · https://creativecommons.org/licenses/by-nc-sa/4.0/
BooksLIB-0918
Algebra in Keilschrift
Høyrup, Jens
AlgebraBS / MS-MPhil / PhD
2021-06-16 · See official DOAB record
BooksLIB-0056
Algebraic Structures and Graph Theory
Cristea, Irina; Bordbar, Hashem
AlgebraADP / BS / MS-MPhil
MDPI - Multidisciplinary Digital Publishing Institute · 2023 · https://creativecommons.org/licenses/by/4.0/
BooksLIB-0057
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets
Ali, Mumtaz; Smarandache, Florentin; Zhang, Xiaohong
AlgebraADP / BS / MS-MPhil
MDPI - Multidisciplinary Digital Publishing Institute · 1st · https://creativecommons.org/licenses/by-nc-nd/4.0/
