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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory/5.05%3A_CyclesThis page defines important graph theory terms such as circuit, cycle, Eulerian circuit, and Hamiltonian circuit. It explains that a circuit is a closed walk with the same starting and ending vertex, ...This page defines important graph theory terms such as circuit, cycle, Eulerian circuit, and Hamiltonian circuit. It explains that a circuit is a closed walk with the same starting and ending vertex, while a cycle does not repeat vertices. An Eulerian circuit covers every edge once, and a Hamiltonian circuit visits each vertex once. Additionally, it offers practice checkpoints for readers to engage with the concepts, including drawing cycles and identifying specific types of circuits.
- https://math.libretexts.org/Courses/Mt._San_Jacinto_College/Ideas_of_Mathematics/03%3A_Set_Theory_and_Logic/3.01%3A_The_BasicsThe concept of sets is a fundamental idea in mathematics. Even at the earliest stage of mathematical reasoning, the idea of sets is being used. As such a fundamental concept, this subject can be stud...The concept of sets is a fundamental idea in mathematics. Even at the earliest stage of mathematical reasoning, the idea of sets is being used. As such a fundamental concept, this subject can be studied on its own as a graduate-level course! Of course, we will not go into such detail as one would expect in such a graduate-level course. Here we will explore some basic definitions and relationships about sets so that we can ultimately apply them to some practical situations.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/07%3A_Appendix/7.02%3A_B_-_NotationThis page includes a table detailing mathematical symbols, their meanings, and first appearances in a book. It covers symbols for numbers, matrices, transformations, vector spaces, and complex numbers...This page includes a table detailing mathematical symbols, their meanings, and first appearances in a book. It covers symbols for numbers, matrices, transformations, vector spaces, and complex numbers, providing readers with a quick reference to understand the notation used in various mathematical concepts.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/08%3A_Appendices/8.02%3A_Well_Ordering_and_InductionThis page introduces summation notation and its applications, emphasizing well-ordered sets and mathematical induction. It explains how summation notation provides a concise representation of sums and...This page introduces summation notation and its applications, emphasizing well-ordered sets and mathematical induction. It explains how summation notation provides a concise representation of sums and describes the principle of well-ordering underlying induction. The section outlines the induction process, including base cases and steps, illustrated by examples that prove formulas and inequalities for all natural numbers.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/03%3A_Sets/3.01%3A_BasicsAn art collector might own a collection of paintings, while a music lover might keep a collection of CDs. Any collection of items can form a set. A set simply specifies the contents; order is not impo...An art collector might own a collection of paintings, while a music lover might keep a collection of CDs. Any collection of items can form a set. A set simply specifies the contents; order is not important. The set represented by {1, 2, 3} is equivalent to the set {3, 1, 2}. Sometimes a collection might not contain all the elements of a set. For example, Chris owns three Madonna albums. While Chris’s collection is a set, we can also say it is a subset of the larger set of all Madonna albums.
