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-COMPLEX-ANALYSIS-VOLUME-I
Complex Analysis — Volume I: Complete Course Book, Theorems, Proofs & Solved Problems
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Complex Analysis / Complex VariablesUniversity / ADP, BS, BSc, MSc and revision
Study Complex Analysis Volume I in 54 chapters with rigorous theorems, proofs, worked examples, solved problems, contour integration, residues and conformal mapping. 54 chapters and 249 A4 pages, with Cauchy theory, series, residues, conformal mapping, harmonic methods, normal families, Picard theorems and Runge approximation.
7 mapped course placements
- ADP Mathematics — Books, Notes & Solutions → Complex Analysis where the programme supports the subject
- BS Mathematics — Books, Notes & Solutions → Complex Analysis / Complex Analysis I / Complex Variables
- Legacy BSc Mathematics — Books, Notes & Solutions → Complex Analysis / Complex Variables
- MSc / Master’s Mathematics — Complex Analysis revision and advanced one-variable function theory
- Mathematics Library — separate owner-resource record
- University Mathematics / Complex Analysis subject family — one canonical child page
- Related from Real Analysis, Calculus, ODE/PDE, Mathematical Physics, Numerical Analysis, Functional Analysis and Topology
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-REAL-ANALYSIS-I
Real Analysis I — Volume I — Complete Solved Notes
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Real Analysis IUniversity / ADP, BS, BSc, MSc and revision
Study Real Analysis I with rigorous definitions, expanded proofs, worked examples and exercises across real numbers, sequences, series, limits, continuity, differentiation, integration and multivariable analysis. Verified structure: 20 chapters, 133 sections, 295 theorem/result boxes and 174 worked examples.
7 mapped course placements
- ADP Mathematics — Real Analysis / Analysis discovery
- BS Mathematics — Real Analysis / Mathematical Analysis
- Legacy BSc Mathematics — Real Analysis revision
- Legacy MSc Mathematics — Real Analysis-I / Analysis revision
- Mathematics Library — separate owner-resource record
- Real Analysis I family — Volume I child card
- Related from Calculus, Topology/Metric Spaces, Numerical Analysis, ODE/PDE and Real Analysis II
Notes & SolutionsTMH-REAL-ANALYSIS-I-VOLUME-III
Real Analysis I — Volume III Complete Solved Notes
Rana Ali Hasan — MPhil Mathematics · Mehreen Kanwal — MPhil Mathematics
Real Analysis IUniversity / ADP, BS, BSc, MSc and revision
Real Analysis I Volume III solved notes with rigorous proofs, worked examples and solved exercises on real numbers, sequences, series, limits, continuity, differentiation and Riemann integration. Verified review structure: 454 A4 pages, 6 chapters, 68 section/exercise pairs and topic exercises solved.
6 mapped course placements
- ADP Mathematics — Real Analysis / Analysis discovery
- BS Mathematics — Real Analysis I / Mathematical Analysis discovery
- Legacy BSc and MSc Mathematics — Real Analysis revision
- Real Analysis I family — Volume III child card
- Mathematics Library — separate owner-resource record
- Related from Calculus, Topology/Metric Spaces, Complex Analysis, Measure Theory and Real Analysis II
Notes & SolutionsTMH-REAL-ANALYSIS-II
Real Analysis II — Complete Course Notes, Proofs & Solved Problems
Mehreen Kanwal — MPhil Mathematics · Rana Ali Hasan — MPhil Mathematics
Real Analysis IIUniversity / BS, BSc, MSc, MS and MPhil revision
A complete 20-chapter Real Analysis II course resource covering rigorous Riemann and Riemann-Stieltjes integration, bounded variation, improper integrals, uniform convergence, power series, approximation, Fourier series, Euclidean spaces, multivariable analysis and multiple Riemann integration.
6 mapped course placements
- BS Mathematics — Real Analysis II / Advanced Analysis discovery
- Legacy BSc / MSc Mathematics — Real Analysis and advanced calculus revision
- ADP Mathematics — relevant analysis overlap where offered
- MS / MPhil Mathematics — rigorous refresher and research preparation
- Mathematics Library — separate owner-resource record
- Related from Calculus, Measure Theory, Functional Analysis and Topology
BooksLIB-0676
A Primer of Real Analysis
Dan Sloughter
Real, Complex & Functional AnalysisBS / MS-MPhil / PhD
Dan Sloughter · 2009 · Attribution-NonCommercial-ShareAlike
BooksLIB-0103
Basic Analysis I: Introduction to Real Analysis
Jiří Lebl
Real, Complex & Functional AnalysisBS / MS-MPhil
Author · Version 6.3 (2026) · CC BY-NC-SA 4.0 or CC BY-SA 4.0
BooksLIB-0104
Basic Analysis II: Introduction to Real Analysis, Volume II
Jiří Lebl
Real, Complex & Functional AnalysisBS / MS-MPhil
Author · Version 6.3 (2026) · CC BY-NC-SA 4.0 or CC BY-SA 4.0
BooksLIB-0635
Basic Analysis: Introduction to Real Analysis
Jirí Lebl
Real, Complex & Functional AnalysisBS / MS-MPhil / PhD
Jirí Lebl · 2016 · Attribution-NonCommercial-ShareAlike
BooksLIB-0193
Elementary Real Analysis
Brian S. Thomson; Judith B. Bruckner; Andrew M. Bruckner
Real, Complex & Functional AnalysisBS / MS-MPhil
Authors · 2nd ed. (2008) · Copyright retained for commercial uses; official free PDF
BooksLIB-0257
How We Got from There to Here: A Story of Real Analysis
Robert Rogers; Eugene Boman
Real, Complex & Functional AnalysisBS
Milne Open Textbooks / Authors · Current open edition · CC BY-NC-SA 3.0
BooksLIB-0285
Introduction to Real Analysis
William F. Trench
Real, Complex & Functional AnalysisBS / MS-MPhil
Author · Current open edition · CC BY-NC-SA 3.0
BooksLIB-0363
Measure, Integration & Real Analysis
Sheldon Axler
Real, Complex & Functional AnalysisMS-MPhil / PhD
Springer / Author · 2020; PDF updated 12 Jun 2026 · Open Access; see book page
Notes & SolutionsUNS-MIT-FOURIER-18103
MIT 18.103 Fourier Analysis — Notes & Eleven Problem Sets
MIT OpenCourseWare
Harmonic AnalysisBS Mathematics; MS / MPhil Mathematics; PhD Mathematics
Fourier-analysis course notes and eleven problem sets.
12 mapped course placements
- Harmonic Analysis — BS Mathematics
- Harmonic Analysis — MS / MPhil Mathematics
- Harmonic Analysis — PhD Mathematics
- Measure Theory — BS Mathematics
- Measure Theory — MS / MPhil Mathematics
- Measure Theory — PhD Mathematics
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — PhD Mathematics
- Integral Transforms — BS Mathematics
- Integral Transforms — MS / MPhil Mathematics
- Integral Transforms — PhD Mathematics
Notes & SolutionsUNS-MIT-INEQ-18014
MIT 18.014 Calculus with Theory — Solved Inequality/Theory Problems
MIT OpenCourseWare
InequalitiesAssociate Degree (AD) Mathematics; BS Mathematics
Rigorous theory problem sets with solutions including inequalities.
6 mapped course placements
- Inequalities — Associate Degree (AD) Mathematics
- Inequalities — BS Mathematics
- Calculus I — Associate Degree (AD) Mathematics
- Calculus I — BS Mathematics
- Real Analysis — Associate Degree (AD) Mathematics
- Real Analysis — BS Mathematics
Notes & SolutionsUNS-MIT-FOURIER-RES18015
MIT Topics in Fourier Analysis 2024 — Notes & Exercise Solutions
MIT OpenCourseWare
Integral TransformsBS Mathematics; MS / MPhil Mathematics; PhD Mathematics
Current 2024 Fourier notes and consolidated solutions PDF.
9 mapped course placements
- Integral Transforms — BS Mathematics
- Integral Transforms — MS / MPhil Mathematics
- Integral Transforms — PhD Mathematics
- Harmonic Analysis — BS Mathematics
- Harmonic Analysis — MS / MPhil Mathematics
- Harmonic Analysis — PhD Mathematics
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — PhD Mathematics
Notes & SolutionsUNS-MC-110
Measure Theory by M Usman Hamid & Saima Akram
MathCity / source contributor
Measure TheoryBS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
Course Notes · Measure Theory · BS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
6 mapped course placements
- Measure Theory — BS Mathematics
- Measure Theory — MS / MPhil Mathematics
- Measure Theory — Legacy MSc Mathematics Resources
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — Legacy MSc Mathematics Resources
Notes & SolutionsUNS-MC-109
Measure Theory Handwritten Notes by Asim Marwat
MathCity / source contributor
Measure TheoryBS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
Handwritten Notes · Measure Theory · BS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
6 mapped course placements
- Measure Theory — BS Mathematics
- Measure Theory — MS / MPhil Mathematics
- Measure Theory — Legacy MSc Mathematics Resources
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — Legacy MSc Mathematics Resources
Notes & SolutionsUNS-MC-108
Measure Theory Notes by Anwar Khan
MathCity / source contributor
Measure TheoryBS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
Course Notes · Measure Theory · BS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
6 mapped course placements
- Measure Theory — BS Mathematics
- Measure Theory — MS / MPhil Mathematics
- Measure Theory — Legacy MSc Mathematics Resources
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — Legacy MSc Mathematics Resources
Notes & SolutionsUNS-MIT-MEAS-18125
MIT 18.125 Measure and Integration — Notes & Problem Sets
MIT OpenCourseWare
Measure TheoryBS Mathematics; MS / MPhil Mathematics; PhD Mathematics
Graduate measure/integration notes and assignments.
6 mapped course placements
- Measure Theory — BS Mathematics
- Measure Theory — MS / MPhil Mathematics
- Measure Theory — PhD Mathematics
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — PhD Mathematics
Notes & SolutionsUNS-MC-069
Advance Analysis by Ms. Iqra Liaqat
MathCity / source contributor
Real AnalysisAssociate Degree (AD) Mathematics; BS Mathematics; MS / MPhil Mathematics; Legacy BSc Mathematics Resources
Course Notes · Real Analysis · Associate Degree (AD) Mathematics; BS Mathematics; MS / MPhil Mathematics; Legacy BSc Mathematics Resources
4 mapped course placements
- Real Analysis — Associate Degree (AD) Mathematics
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — Legacy BSc Mathematics Resources
Notes & SolutionsUNS-MC-068
Advanced Analysis: Handwritten Notes
MathCity / source contributor
Real AnalysisBS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
Handwritten Notes · Real Analysis · BS Mathematics; MS / MPhil Mathematics; Legacy MSc Mathematics Resources
3 mapped course placements
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — Legacy MSc Mathematics Resources
Notes & SolutionsUNS-MC-100
Handwritten Notes of Real Analysis by Asim Marwat
MathCity / source contributor
Real AnalysisAssociate Degree (AD) Mathematics; BS Mathematics; MS / MPhil Mathematics; Legacy BSc Mathematics Resources
Handwritten Notes · Real Analysis · Associate Degree (AD) Mathematics; BS Mathematics; MS / MPhil Mathematics; Legacy BSc Mathematics Resources
4 mapped course placements
- Real Analysis — Associate Degree (AD) Mathematics
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — Legacy BSc Mathematics Resources
Notes & SolutionsUNS-MC-117
Metric Spaces (Notes)
MathCity / source contributor
Real AnalysisAssociate Degree (AD) Mathematics; BS Mathematics; MS / MPhil Mathematics; Legacy BSc Mathematics Resources
Course Notes · Real Analysis · Associate Degree (AD) Mathematics; BS Mathematics; MS / MPhil Mathematics; Legacy BSc Mathematics Resources
8 mapped course placements
- Real Analysis — Associate Degree (AD) Mathematics
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
- Real Analysis — Legacy BSc Mathematics Resources
- Topology — Associate Degree (AD) Mathematics
- Topology — BS Mathematics
- Topology — MS / MPhil Mathematics
- Topology — Legacy BSc Mathematics Resources
Notes & SolutionsUNS-MIT-RA-100B
MIT 18.100B Analysis I — Problem Set Solutions
MIT OpenCourseWare
Real AnalysisBS Mathematics; MS / MPhil Mathematics
Official solved analysis problem sets.
2 mapped course placements
- Real Analysis — BS Mathematics
- Real Analysis — MS / MPhil Mathematics
