{"id":19921019,"url":"https://github.com/hacker-code-j/modern-mathematics","last_synced_at":"2026-02-22T09:02:49.800Z","repository":{"id":246872529,"uuid":"819977913","full_name":"Hacker-Code-J/Modern-Mathematics","owner":"Hacker-Code-J","description":"Materials for graduate-level mathematics, including topics like set theory, real analysis, topology, linear algebra and abstract algebra. 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The content is structured in TeX documents, which include detailed notes, diagrams, and proofs.\n\n## Structure\n\n### Core Materials (`grad-math-full`)\nThis directory is the core of the repository, featuring detailed documents for various topics in graduate-level mathematics:\n- `grad-math-[n].tex`: Main source files for each topic.\n- `grad-math-[n].pdf`: Compiled PDFs from the TeX files.\n\n#### Topics Covered in the `grad-math-full` Folder\n\nThe `grad-math-full` directory contains detailed documents for graduate-level mathematics courses, organized by specific topics in each document:\n\n---\n##### Set Theory\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-1.tex/pdf\u003c/strong\u003e: Set Theory I\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eSet, Power Set, Cartesian Product\u003c/li\u003e\n\u003cli\u003eUnion, Intersection, Complement\u003c/li\u003e\n\u003cli\u003eFunction, Image, Pre-image\u003c/li\u003e\n\u003cli\u003eInjection, Surjection, Bijection\u003c/li\u003e\n\u003cli\u003eAxiom of Choice\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-2.tex/pdf\u003c/strong\u003e: Set Theory II\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eRelation, Equivalence Relation\u003c/li\u003e\n\u003cli\u003eEquivalence Class, Partition\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n##### Advanced Calculus and Topology\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-3.tex/pdf\u003c/strong\u003e: Advanced Calculus I\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eBoundedness, Supremum and Infimum\u003c/li\u003e\n\u003cli\u003eLeast Upper Bound Property (Completeness Axiom)\u003c/li\u003e\n\u003cli\u003eWell-Ordering Principle and Mathematical Induction\u003c/li\u003e\n\u003cli\u003eArchimedean Property\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-4.tex/pdf\u003c/strong\u003e: Advanced Calculus II\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eConvergence of Sequences\u003c/li\u003e\n\u003cli\u003eInequality Rule for Absolute Values\u003c/li\u003e\n\u003cli\u003eLimit Theorem (Algebraic Property of Limit of Sequence)\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-5.tex/pdf\u003c/strong\u003e: Topology I\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eTopology and Topological Space\u003c/li\u003e\n\u003cli\u003eOpen Set\u003c/li\u003e\n\u003cli\u003eContinuous Mapping\u003c/li\u003e\n\u003cli\u003eDistance Function and Metric Space\u003c/li\u003e\n\u003cli\u003eConvergence of Sequences; Continuity of Functions\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-6.tex/pdf\u003c/strong\u003e: Advanced Calculus III\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eLimit of a Function\u003c/li\u003e\n\u003cli\u003eContinuity of a Function\u003c/li\u003e\n\u003cli\u003eMonotone Convergent Theorem (MCT)\u003c/li\u003e\n\u003cli\u003eNested Interval Property (NIP)\u003c/li\u003e\n\u003cli\u003eBolzano-Weierstrass Theorem\u003c/li\u003e\n\u003cli\u003eLimit Superior and Limit Inferior\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n##### Linear Algebra and Abstract Algebra\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-7.tex/pdf\u003c/strong\u003e: Algebraic Structures \u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eGroup\u003c/li\u003e\n\u003cli\u003eRing\u003c/li\u003e\n\u003cli\u003eField\u003c/li\u003e\n\u003cli\u003eModule\u003c/li\u003e\n\u003cli\u003eVector Space\u003c/li\u003e\n\u003cli\u003eAlgebra\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-8.tex/pdf\u003c/strong\u003e: Linear Algebra I \u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eLinear Combination, Spanning Set\u003c/li\u003e\n\u003cli\u003eLinearly Independent and Dependent\u003c/li\u003e\n\u003cli\u003e(Hamel) Basis\u003c/li\u003e\n\u003cli\u003ePartial Order, POSET\u003c/li\u003e\n\u003cli\u003eTotal Order (Linear Order), TOSET\u003c/li\u003e\n\u003cli\u003eMaximal, Minimal, Hasse Diagram\u003c/li\u003e\n\u003cli\u003eChain, Zorn's Lemma\u003c/li\u003e\n\u003cli\u003eHamel Basis Theorem (Existence of Basis)\u003c/li\u003e\n\u003cli\u003eInvariance of Basis Cardinality; Dimension of Vector Space\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-9.tex/pdf\u003c/strong\u003e: Linear Algebra II \u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eUniqueness of Representation with respect to a Basis; Coordinate\u003c/li\u003e\n\u003cli\u003eLinear Transformation\u003c/li\u003e\n\u003cli\u003eVector Space Isomorphism (Linear Isomorphism)\u003c/li\u003e\n\u003cli\u003eClassification of Vector Space (up to Isomorphism)\u003c/li\u003e\n\u003cli\u003eMatrix Representation of a Linear Transformation\u003c/li\u003e\n\u003cli\u003eTBA\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-10.tex/pdf\u003c/strong\u003e: Linear Algebra to Abstract Algebra\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eSubspace; Span\u003c/li\u003e\n\u003cli\u003eSubgroup\u003c/li\u003e\n\u003cli\u003eHomomorphism; Monomorphism; Epimorphism\u003c/li\u003e\n\u003cli\u003eIsomorphism\u003c/li\u003e\n\u003cli\u003eKernel and Image\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-11.tex/pdf\u003c/strong\u003e: Abstract Algebra I\u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eCyclic Group\u003cli\u003e\n\u003cli\u003eTBA\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n\u003cdetails\u003e\n\u003csummary\u003e\u003cstrong\u003egrad-math-12.tex/pdf\u003c/strong\u003e: Abstract Algebra II (TBA) \u003c/summary\u003e\n\u003cul\u003e\n\u003cli\u003eTBA\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/details\u003e\n\n---\n\nEach `.tex` file is accompanied by a `.pdf` version which is the compiled and formatted version of the LaTeX document. These documents provide an in-depth look at the fundamental and advanced topics necessary for graduate-level studies in mathematics.\n\n\u003c!--\n### Supplementary Materials\n- `abstract-algebra/`: Additional notes and resources on abstract algebra.\n- `chapter/`: Chapter-wise breakdown of topics.\n- `code/`: Example codes, primarily in SageMath, for computational mathematics.\n- `preamble/`, `tikz/`, and other directories: Contain various support files like LaTeX preamble settings, TikZ diagrams, custom LaTeX commands, and theorem environments.\n\n### Practice and Examples\n- `tikz/`: Extensive examples of mathematical diagrams created using TikZ.\n- `latex-practice.tex`: A document to practice LaTeX skills.\n\n### Documentation\n- `README.md`: This file.\n- `LICENSE`: Licensing information for the use of this repository.\n--\u003e\n\n## Usage\n\nTo compile the documents, you need a TeX distribution such as TeX Live:\n1. Install TeX Live: [Installation Guide](https://www.tug.org/texlive/acquire.html).\n2. Navigate to the desired directory.\n3. Use the command `pdflatex \u003cfile-name.tex\u003e` to compile a file to PDF.\n\n## Contributing\n\nContributions to the repository are welcome. To contribute:\n1. Fork the repository.\n2. Create a new branch for your changes.\n3. Make your changes.\n4. Submit a pull request.\n\n## License\n\nThis repository is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhacker-code-j%2Fmodern-mathematics","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fhacker-code-j%2Fmodern-mathematics","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhacker-code-j%2Fmodern-mathematics/lists"}