Introduction

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This website serves as a centralized hub for a collection of notebooks used in various courses offered by Johns Hopkins University. Free feel to explore a diverse range of materials designed to enhance your understanding of mathematics and computer science.

Mathematics

📘   Algebra Notebooks

📘   Analysis Notebooks

📘   Topology Notebooks

Algebra Notebooks

📘   AS.110.411/412 Honors Algebra I/II

  • Course Description: (Algebra I) An introduction to the basic notions of modern algebra for students with some prior acquaintance with abstract mathematics. Elements of group theory: groups, subgroups, normal subgroups, quotients, homomorphisms. Generators and relations, free groups, products, abelian groups, finite groups. Groups acting on sets, the Sylow theorems. Definition and examples of rings and ideals.
  • Course Description: (Algebra II) A continuation of 110.411 Honors Algebra I. Topics studies include principal ideal domains, structure of finitely generated modules over them. Introduction to field theory. Linear algebra over a field. Field extensions, constructible polygons, non-trisectability. Splitting field of a polynomial, algebraic closure of a field. Galois theory: correspondence between subgroups and subfields. Solvability of polynomial equations by radicals.

  • Last Updated: May 17, 2024
  • Link to Notebook

📘   AS.110.304 Elementary Number Theory

  • Course Description: The student is provided with many historical examples of topics, each of which serves as an illustration of and provides a background for many years of current research in number theory. Primes and prime factorization, congruences, Euler's function, quadratic reciprocity, primitive roots, solutions to polynomial congruences (Chevalley's theorem), Diophantine equations including the Pythagorean and Pell equations, Gaussian integers, Dirichlet's theorem on primes.

  • Last Updated: Jan 14, 2024
  • Link to Notebook

📘   AS.110.212 Honors Linear Algebra

  • Course Description: This is a course in the study of linear spaces, or vector spaces, and the structure of linear mappings between such spaces. Topics include vector spaces, the structure of linear transformations and matrices, eigenvalues and eigenvectors, the Jordan canonical form, inner product spaces and linear operators, and determinants.

  • Last Updated: Jan 14, 2024
  • Link to Notebook

Analysis Notebooks

📘   AS.110.415 Honors Analysis I

  • Course Description: (Analysis I) The important topics to be addressed will be: construction of real numbers, basic topology, numerical sequences and series, continuity and differentiation, sequences and series of functions, and uniform convergence.
  • Course Description: (Analysis II) Continuation of AS.110.415, introduction to real analysis. Topics include Lebesgue integration and differentiation. Elementary Hilbert and Banach space theory. Baire category theorem.

  • Last Updated: May 17, 2024
  • Link to Notebook

Topology Notebooks

📘   AS.110.413 Introduction to Topology

  • Course Description: Topological spaces, connectedness, compactness, quotient spaces, metric spaces, function spaces. An introduction to algebraic topology: covering spaces, the fundamental group, and other topics as time permits.

  • Last Updated: Jan 14, 2024
  • Link to Notebook

Computer Science

📘   EN.601.433 Intro Algorithms

  • Course Description: This course concentrates on the design of algorithms and the rigorous analysis of their efficiency. topics include the basic definitions of algorithmic complexity (worst case, average case); basic tools such as dynamic programming, sorting, searching, and selection; advanced data structures and their applications (such as union-find); graph algorithms and searching techniques such as minimum spanning trees, depth-first search, shortest paths, design of online algorithms and competitive analysis.

  • Last Updated: Jan 14, 2024
  • Link to Notebook

📘   EN.601.475 Machin Learning

  • Course Description: Machine learning is subfield of computer science and artificial intelligence, whose goal is to develop computational systems, methods, and algorithms that can learn from data to improve their performance. This course introduces the foundational concepts of modern Machine Learning, including core principles, popular algorithms and modeling platforms. This will include both supervised learning, which includes popular algorithms like SVMs, logistic regression, boosting and deep learning, as well as unsupervised learning frameworks, which include Expectation Maximization and graphical models.

  • Last Updated: Jan 14, 2024
  • Link to Notebook