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Combined display of all available logs of Department of Mathematics at UTSA. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
(newest | oldest) View (newer 250 | older 250) (20 | 50 | 100 | 250 | 500)- 09:51, 29 March 2023 Juan.gutierrez3 talk contribs created page Machine Learning and Pattern Recognition in AI (Created page with "Lesson 9 of MDC1213 Slide 1: Title Slide Machine Learning and Pattern Recognition in AI Slide 2: Course Overview Brief summary of the course objectives and les...")
- 09:50, 29 March 2023 Juan.gutierrez3 talk contribs created page Cultural Bias in Data Collection and Interpretation (Created page with "Lesson 8 of MDC1213 Slide 1: Title Slide Cultural Bias in Data Collection and Interpretation Slide 2: Course Overview Brief summary of the course objectives an...")
- 09:49, 29 March 2023 Juan.gutierrez3 talk contribs created page Statistics and Probability: Interpreting Data and Predicting Outcomes (Created page with "Lesson 7 of MDC1213 Slide 1: Title Slide Statistics and Probability: Interpreting Data and Predicting Outcomes Slide 2: Course Overview Brief summary of the co...")
- 09:49, 29 March 2023 Juan.gutierrez3 talk contribs created page The Art of Problem Solving: Creativity in Mathematics (Created page with "Lesson 6 of MDC1213 Slide 1: Title Slide The Art of Problem Solving: Creativity in Mathematics Slide 2: Course Overview Brief summary of the course objectives...")
- 09:48, 29 March 2023 Juan.gutierrez3 talk contribs created page The Language of Mathematics: Symbols, Expressions, and Equations (Created page with "Lesson 5 of MDC1213 Slide 1: Title Slide The Language of Mathematics: Symbols, Expressions, and Equations Slide 2: Course Overview Brief summary of the course...")
- 09:46, 29 March 2023 Juan.gutierrez3 talk contribs created page The Role of Artificial Intelligence in Understanding Human Behavior (Created page with "=The Role of Artificial Intelligence in Understanding Human Behavior= Lesson 4 of MDC1213 Slide 1: Title Slide The Role of Artificial Intelligence in Understanding...")
- 09:44, 29 March 2023 Juan.gutierrez3 talk contribs created page How Data Science Has Shaped Society and Culture (Created page with "=How Data Science Has Shaped Society and Culture= Lesson 3 of MDC1213 Slide 1: Title Slide How Data Science Has Shaped Society and Culture Slide 2: Course Overview...")
- 09:43, 29 March 2023 Juan.gutierrez3 talk contribs created page The Historical Evolution of Mathematics in Cultural Context (Created page with "= The Historical Evolution of Mathematics in Cultural Context = Lesson 2 of MDC1213 Slide 1: Title Slide The Historical Evolution of Mathematics in Cultural Context...")
- 09:39, 29 March 2023 Juan.gutierrez3 talk contribs created page Introduction to Mathematics, Data Science, and Artificial Intelligence (Created page with "= Introduction to Mathematics, Data Science, and Artificial Intelligence = Lesson 1 of MDC1213 Slide 1: Title Introduction to Mathematics, Data Science, and Artific...")
- 09:37, 29 March 2023 Juan.gutierrez3 talk contribs created page MDC1213 (Created page with "= Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context = Course Description: This introductory survey course for freshmen aims to explore...")
- 22:00, 25 March 2023 Jose.iovino talk contribs created page MAT5113 (Created page with "'''Catalog entry''' ''Prerequisite'': MAT 1313 Algebra and Number Systems. ''Content:'' Project-based modular course allowing individualized learning of computer tools and s...")
- 14:55, 25 March 2023 Jose.iovino talk contribs created page MAT4423/MAT5443 (Created page with "'''Catalog description''' ''Prerequisites'': MAT 1214 and MAT 3013. ''Content'': Axiomatizations of propositional logic, axiomatizations of first-order logic, completeness...")
- 12:49, 25 March 2023 Eduardo.duenez talk contribs created page MAT3333 (MAT3333 page created.)
- 12:44, 25 March 2023 Eduardo.duenez talk contribs created page MAT3313 (Renamed page to remove space.)
- 21:48, 24 March 2023 Jose.iovino talk contribs created page MAT4283 (Created page with "'''Catalog entry''': Prerequisite: MAT 1313 Algebra and Number Systems. Project-based modular course allowing individualized learning of computer tools and skills most relev...")
- 21:44, 24 March 2023 Jose.iovino talk contribs created page MAT 3313 (Created page with "'''Catalog description''' ''Prerequisites'': MAT 1214 and MAT 3013. ''Content'': Axiomatizations of propositional logic, axiomatizations of first-order logic, completeness...")
- 18:29, 24 March 2023 Jose.iovino talk contribs created page MAT4033 (Created page with "Introduction to the theory of finite-dimensional vector spaces. '''Sample textbook''': [1] M. Thamban Nair · Arindama Singh, ''Linear Algebra'', 2008. Freely available to...")
- 15:27, 24 March 2023 Jose.iovino talk contribs created page MAT3003 (Created page with "Introduction to basic discrete structures. '''Sample textbooks''': [1] Gordon Pace, ''Mathematics of Discrete Structures foe Computer Science'', Springer, 2012 [2] Vladle...")
- 08:40, 24 March 2023 Juan.gutierrez3 talk contribs created page MAT4373 (Redirected page to MAT5373) Tag: New redirect
- 08:39, 24 March 2023 Juan.gutierrez3 talk contribs created page MAT5373 (Created page with "=Mathematical Statistics - MAT4173/5373= {| class="wikitable" | Session || Section || Date || Topic |- | 1 || 1.1 || 6/5/2017 || Populations and Samples |- | 2 || 1.2 || 6/...")
- 07:12, 24 March 2023 Juan.gutierrez3 talk contribs created page MAT4133 (Created redirection to MAT5133) Tag: New redirect
- 13:26, 23 March 2023 Eduardo.duenez talk contribs created page MAT5323 (Textbook and short contents table.)
- 13:22, 23 March 2023 Eduardo.duenez talk contribs created page MAT5123 (MAT5123 is Crypto I.)
- 07:27, 23 March 2023 Duynguyenvu.hoang talk contribs created page MAT4143 (Created page with "==Course description== Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding or mathematical methods used i...")
- 09:48, 22 March 2023 Jose.iovino talk contribs created page MAT5133 (Created page with "Introduction to post-quantum Cryptography.")
- 15:23, 18 March 2023 Jose.iovino talk contribs created page MAT5433 (Created page with "Introduction to basic discrete structures. '''Sample textbooks''': [1] Vladlen Koltun, ''Discrete Structures, Lecture Notes, Stanford University'', 2008. Freely available...")
- 14:25, 18 March 2023 Jose.iovino talk contribs created page MAT5423 (Created page with "Introduction to basic discrete structures. Sample textbooks: [1] Gordon Pace, ''Mathematics of Discrete Structures foe Computer Science'', Springer, 2012 [2] Vladlen Koltu...")
- 08:05, 14 March 2023 Duynguyenvu.hoang talk contribs created page MAT 5653 (Created page with "==Topics List== {| class="wikitable sortable" ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |- |Week 1 || * || Basic Concepts of Ordinary D...")
- 08:20, 13 March 2023 Duynguyenvu.hoang talk contribs created page AIM 5113 (Created page with "==Topics List== {| class="wikitable sortable" ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |- |Week 1 || * || Introduction to statistical...")
- 17:06, 10 March 2023 Duynguyenvu.hoang talk contribs created page MAT5143 (Created Math Phys page)
- 14:23, 10 March 2023 Duynguyenvu.hoang talk contribs created page MAT 5673 (Created page for PDE1.)
- 20:38, 9 March 2023 Jose.iovino talk contribs created page MAT5173 (Created page with "The opportunity for development of basic theory of algebraic structures. Areas of study may include monoids, semigroups, groups, isomorphism theorems, free groups, group exten...")
- 17:25, 9 March 2023 Jose.iovino talk contribs created page MAT5183 (Created page with "Special topics in algebra.")
- 17:25, 9 March 2023 Jose.iovino talk contribs created page MAT5253 (Created page with "Special topics in general topology.")
- 15:49, 9 March 2023 Jose.iovino talk contribs created page MAT5002 (Created page with "(1) Partially ordered sets, extreme elements (maximum, minimum, maximal and minimal elements), lattices, boolean algebras, circuit design. (2) Combinatorics: Basic counting t...")
- 15:36, 9 March 2023 Jose.iovino talk contribs created page MAT5243 (Created page with "Review of metric spacxes, general topological spaces, continuous functions, the product topology, filters and nets, compactness, connected spaces.")
- 15:30, 9 March 2023 Jose.iovino talk contribs created page MAT4XXX/5XXX (Created page with "This course is intended to develop practical marketable skills in data analytics using rigorous mathematical methodologies via SQL, Python and Git. The mathematical topics cov...")
- 15:26, 9 March 2023 Jose.iovino talk contribs created page MAT5003 (Created page with "Structures, theories, models, compactness, spaces of types, real-valued logic.")
- 15:05, 9 March 2023 Jose.iovino talk contribs created page MAT5213 (Created page with "Introduction to abstract measure theory and integration.")
- 15:04, 9 March 2023 Jose.iovino talk contribs created page MAT5223 (Created page with "Congruences and residue class rings, Fermat’s Little Theorem, the Euler phi-function, the Chinese Remainder Theorem, complexity, symmetric-key cryptosystems, cyclic groups,...")
- 15:02, 9 March 2023 Jose.iovino talk contribs created page MAT5203 (Created page with "Introduction to Lebesgue measure and integration.")
- 14:56, 9 March 2023 Jose.iovino talk contribs created page MAT4002 (Created page with "(1) Basic counting, generating functions, Inclusion-Exclusion Principle (2) Order relations: Partially ordered sets, totally ordered sets, extreme elements (maximum, minimum,...")
- 14:50, 9 March 2023 Jose.iovino talk contribs created page MAT5001 (Created page with "(1) Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms. (2) Predicat...")
- 14:45, 9 March 2023 Jose.iovino talk contribs created page MAT5283 (Created page with " A study of linear algebraic structures that may include linear transformations, inner product spaces, eigenvalues, Cayley-Hamilton theorem, similarity, the Jordan canonical f...")
- 14:37, 9 March 2023 Jose.iovino talk contribs created page MAT4353 (Created page with "Congruences and residue class rings, Fermat’s Little Theorem, the Euler phi-function, the Chinese Remainder Theorem; complexity; symmetric-key cryptosystems; cyclic groups,...")
- 14:24, 9 March 2023 Jose.iovino talk contribs created page MATxxx (Created page with "1. Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms. 2. Predicate...")
- 14:49, 8 March 2023 Juan.gutierrez3 talk contribs created page MAT2213 (Created page with "==Topics List== {| class="wikitable sortable" ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |- |Week 1 || <div style="text-align:...")
- 14:48, 8 March 2023 Juan.gutierrez3 talk contribs created page MAT1223 (Created page with "The textbook for this course is [https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.] A comprehensive list of al...")
- 14:48, 8 March 2023 Juan.gutierrez3 talk contribs created page MAT1213 (Created page with "The textbook for this course is [https://openstax.org/details/calculus-volume-1 Calculus (Volume 1) by Gilbert Strang, Edwin Herman, et al.] A comprehensive list of all unde...")
- 16:36, 10 February 2023 User account Jose.palacios talk contribs was created by Juan.gutierrez3 talk contribs
- 16:34, 10 February 2023 User account Spalding.garakani talk contribs was created by Juan.gutierrez3 talk contribs
- 14:51, 16 December 2022 Juan.gutierrez3 talk contribs created page MAT2313 (Created page with "Foundations of Mathematics (3-0) 3 Credit Hours ==Course Catalog== 3 Credit Hours. Corequisite: MAT1224. Permutations, combinations, multinational coefficients, inclusion...")
- 11:57, 6 February 2022 Khanh talk contribs created page Measurement (AREA) (Created page with "right|thumb|alt=Three shapes on a square grid|The combined area of these three shapes is approximately 15.57 squares. '''Area''' is the quantity that expres...")
- 21:48, 5 February 2022 Khanh talk contribs created page Mathematical & Statistical Reasoning (Created page with "'''Statistical inference''' is the process of using data analysis to infer properties of an underlying distribution of probability. '''Inferential statistical analysis''' infe...")
- 13:17, 5 February 2022 Khanh talk contribs created page Number Systems, Base 10, 5 and 2 (Created page with "264px|thumb|right|Numbers written in different numeral systems. A '''numeral system''' (or '''system of numeration''') is a writin...")
- 21:23, 4 February 2022 Khanh talk contribs created page Problem Solving Introduction (Created page with "== Licensing == Content obtained and/or adapted from: * [https://en.wikipedia.org/wiki/Base_ten_block Base ten block, Wikipedia] under a CC BY-SA license https://en.wikipedi...")
- 16:37, 29 January 2022 Khanh talk contribs created page Linear Transformations (Created page with "==Linear Transformations== <blockquote style="background: white; border: 1px solid black; padding: 1em;"> :'''Definition:''' A transformation <math>T: \mathbb{R}^n \to \mathb...")
- 14:11, 29 January 2022 Khanh talk contribs created page Orthogonal Transformations and Orthogonal Matrices (Created page with "== Licensing == Content obtained and/or adapted from: * [https://en.wikipedia.org/wiki/Orthogonal_transformation Orthogonal transformation, Wikipedia] under a CC BY-SA licens...")
- 13:43, 29 January 2022 Khanh talk contribs created page Cramer's Rule (Created page with "In linear algebra, '''Cramer's rule''' is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system ha...")
- 15:12, 23 January 2022 Khanh talk contribs created page Completeness (Created page with "'''Completeness''' and related ideas inherently assume the notion of 'distance'. Hence, throughout this chapter, we will be dealing only with metric spaces. ===Definition===...")
- 13:23, 23 January 2022 Khanh talk contribs created page Subspaces of Metric Spaces (Created page with "{{Redirect|Induced topology|the topology generated by a family of functions|Initial topology}} In topology and related areas of mathematics, a '''subspace''' of a t...")
- 13:14, 23 January 2022 Khanh talk contribs created page Cartesian Products of Metric Spaces (Created page with "In mathematics, a '''product metric''' is a metric on the Cartesian product of finitely many metric spaces <math>(X_1,d_{X_1}),\ldots,(X_n,d_{X_n})</math> which metrizes the p...")
- 12:55, 23 January 2022 Khanh talk contribs created page Continuous Mappings Between Metric Spaces (Created page with "== An Open Set == ===Definition=== A set is said to be '''open''' in a metric space if it equals its interior (<math> A = Int(A)</math>). When we encounter topological spaces...")
- 15:27, 12 January 2022 Khanh talk contribs created page The Definition of the Limit of a Function (Created page with "In mathematics, the '''limit of a function''' is a fundamental concept in calculus and analysis concerning the behavior of that Function (m...")
- 15:11, 12 January 2022 Khanh talk contribs created page Functions:Range (Created page with "In mathematics, the '''range of a function''' may refer to either of two closely related concepts: * The codomain of the function * The image of the function Given two sets...")
- 14:28, 12 January 2022 Khanh talk contribs created page Derivative Properties (Created page with "This is a summary of '''differentiation rules''', that is, rules for computing the derivative of a function in calculus. == Elementary rules of differentiation == Unless oth...")
- 16:17, 11 January 2022 Khanh talk contribs created page Vectors, Matrices, and Gauss-Jordan Elimination (Created page with " File:Matris.png|thumb|An {{math|''m'' × ''n''}} matrix: the {{math|''m''}} rows are horizontal and the {{math|''n''}} columns are vertical. Each element of a matrix i...")
- 16:52, 9 January 2022 Khanh talk contribs created page Continuity and Gauges (Created page with "= Continuity = The integral form of the continuity equation states that: * The amount of {{math|''q''}} in a region increases when additional {{math|''q''}} flows inward thro...")
- 16:38, 9 January 2022 Khanh talk contribs created page Derivatives (Created page with " ==What is Differentiation?== Differentiation is a process of finding a function that outputs the '''rate of change''' of one variable with respect to another variable. Infor...")
- 12:07, 9 January 2022 Khanh talk contribs created page Abstract Algebra: Homomorphisms (Created page with "In algebra, a '''homomorphism''' is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The wor...")
- 11:50, 9 January 2022 Khanh talk contribs created page Cognitive Guided Instruction (Created page with " thumb|primary/elementary mathematics symbols '''Elementary arithmetic''' is the simplified portion of arithmetic that includes the operat...")
- 23:47, 8 January 2022 Khanh talk contribs created page Base 10, Base 2 & Base 5 (Created page with "In a positional numeral system, the '''radix''' or '''base''' is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal...")
- 18:24, 8 January 2022 Khanh talk contribs created page Whole numbers subtraction models and properties (Created page with "right|thumb|180px|"5 − 2 = 3" (verbally, "five minus two equals three") '''Subtraction''' is an arithmetic operation that represents the operation...")
- 18:05, 8 January 2022 Khanh talk contribs created page Whole numbers addition models and properties (Created page with "right|thumb|120px|3 + 2 = 5 with apples, a popular choice in textbooks '''Addition''' (usually signified by the plus symbol +) is one of the four basic...")
- 17:31, 8 January 2022 Khanh talk contribs created page Whole numbers division models and properties (Created page with "In arithmetic, '''long division''' is a standard division algorithm suitable for dividing multi-digit Arabic numerals (Positional notation) that is simple enough to perform by...")
- 16:42, 8 January 2022 Khanh talk contribs created page Whole numbers multiplication models and properties (Created page with "thumb|right|Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). File:Multiply scaling.svg|thumb|right|Multiplicat...")
- 15:50, 8 January 2022 Khanh talk contribs created page Multiplication and division of integers (Created page with "== Multiplication of Integers == :<math>N\times M</math> is the sum of ''N'' copies of ''M'' when ''N'' and ''M'' are positive whole numbers. This gives the number of things...")
- 14:57, 8 January 2022 Khanh talk contribs created page Division Algorithms (Created page with "thumb|20 / 4 = 5, illustrated here with apples. This is said verbally, "Twenty divided by four equals five." '''Division''' is one of the four basic...")
- 13:38, 8 January 2022 Khanh talk contribs created page Multiplication Algorithms (Created page with "thumb|right|Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). File:Multiply scaling.svg|thumb|right|Multiplicat...")
- 23:14, 7 January 2022 Khanh talk contribs created page Subtraction Algorithms (Created page with "right|thumb|180px|"5 − 2 = 3" (verbally, "five minus two equals three") <div class="tright">{{Arithmetic operations}}</div> File:Shop placard sh...")
- 22:50, 7 January 2022 Khanh talk contribs created page Addition and subtraction of integers (Created page with "== Addition Integers == The simplest conception of an integer is that it consists of an absolute value (which is a natural number) and a sign (gene...")
- 17:16, 7 January 2022 Khanh talk contribs created page Addition Algorithms (Created page with "right|thumb|120px|3 + 2 = 5 with apples, a popular choice in textbooks '''Addition''' (usually signified by the plus symbol {{char|+}}) is one of the f...")
- 14:50, 7 January 2022 Khanh talk contribs created page Fractions meaning and models (Created page with "thumb|A cake with one quarter (one fourth) removed. The remaining three fourths are shown by dotted lines and labeled by the fraction {{sfrac|1|4}}....")
- 16:10, 5 January 2022 Khanh talk contribs created page Number Theory (Created page with "File:Spirale Ulam 150.jpg|thumb|250x250px|The distribution of prime numbers is a central point of study in number theory. This Ulam spiral serves to illustrate it, hinting,...")
- 15:42, 5 January 2022 Khanh talk contribs created page The Structure of Groups (Created page with "thumb|The popular puzzle Rubik's cube invented in 1974 by Ernő Rubik has been used as an illustration of permutation groups. In mathematics and ab...")
- 18:56, 19 December 2021 Khanh talk contribs created page Normal Subgroups and Factor Groups (Created page with "In abstract algebra, a '''normal subgroup''' (also known as an '''invariant subgroup''' or '''self-conjugate subgroup''') is a subgroup that is invariant under conjugation by...")
- 18:31, 19 December 2021 Khanh talk contribs created page Integral Domains (Created page with "In mathematics, specifically abstract algebra, an '''integral domain''' is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral dom...")
- 16:50, 19 December 2021 Khanh talk contribs created page Polynomials (Created page with "In mathematics, especially in the field of algebra, a '''polynomial ring''' or '''polynomial algebra''' is a ring (which is also a commutative...")
- 00:06, 19 December 2021 Khanh talk contribs created page Rings (Created page with " {{Ring theory sidebar}} In mathematics, '''rings''' are algebraic structures that generalize fields: multiplication need not be commutativ...")
- 11:44, 18 December 2021 Khanh talk contribs created page Homomorphisms (Created page with "In algebra, a '''homomorphism''' is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The wor...")
- 01:07, 18 December 2021 Khanh talk contribs created page Isomorphisms (Created page with "In mathematics, an '''isomorphism''' is a structure-preserving mapping between two structures of the same type that can be...")
- 22:02, 17 December 2021 Khanh talk contribs created page Display of Numerical Data (Created page with "https://en.wikipedia.org/wiki/List_of_graphical_methods https://en.wikipedia.org/wiki/Statistical_graphics")
- 21:31, 17 December 2021 Khanh talk contribs created page Display of Categorical Data (Created page with "== Categorical variable == In statistics, a '''categorical variable''' (also called '''qualitative variable''') is a variable that can take on one of a limited, and usually f...")
- 15:47, 16 December 2021 Khanh talk contribs created page Measurement (AREA) – CONVERSION (Created page with "===Area=== {| class="wikitable" |+ Area !Name of unit !Symbol !Definition !Relation to SI units |- | acre (international) || ac | ≡ {{nowrap|1 ch × 10...")
- 14:26, 16 December 2021 Khanh talk contribs created page Measurement (LINEAR) – CONVERSION (Created page with "{{short description|Comparison of various scales}} '''Conversion of units''' is the conversion between different units of measurement for the same quantity, typically...")
- 14:02, 16 December 2021 Khanh talk contribs created page Measurement (LINEAR) (Created page with "thumb|A typical tape measure with both metric and imperial units and two US pennies for comparison '''Measurement''' is the quantification...")
- 13:14, 15 December 2021 Khanh talk contribs created page Perimeter Area (Created page with "right|thumb|alt=Three shapes on a square grid|The combined area of these three shapes is approximately 15.57 squares. '''Area''' is the quantity that expres...")
- 01:29, 15 December 2021 Khanh talk contribs created page Rigid Transformations (Created page with "== Licensing == Content obtained and/or adapted from: * [https://en.wikipedia.org/wiki/Rigid_transformation Rigid transformation, Wikipedia] under a CC BY-SA license")
- 01:09, 15 December 2021 Khanh talk contribs created page Area of Polygons - Formulas (Created page with "== Area of Polygons == File:ParallelogramArea.svg|thumb|180px|alt=A diagram showing how a parallelogram can be re-arranged into the shape of a rectangle|A parallelogram can...")
- 18:58, 12 December 2021 Khanh talk contribs created page Symmetry (Created page with "thumb|A drawing of a butterfly with [[bilateral symmetry, with left and right sides as mirror images of each other.]] In geometry, an objec...")
- 18:40, 12 December 2021 Khanh talk contribs created page Similarity (Created page with "thumb|upright=0.75|Similar figures In Euclidean geometry, two objects are '''similar''' if they have the same shape, or one has the same shape as the...")
- 17:52, 12 December 2021 Khanh talk contribs created page Definitions and Hierarchy of Quadrilaterals (Created page with "A '''quadrilateral''' is a polygon in Euclidean plane geometry with four edges (sides) and four vertices (corners). Other names for quadrilateral include '''quadrangle''' (in...")
- 16:40, 12 December 2021 Khanh talk contribs created page Triangle Congruence (Created page with "File:Congruent non-congruent triangles.svg|thumb|Congruent non-congruent triangles|An example of congruence. The two triangles on the left are congruent, while the third is...")
- 14:52, 12 December 2021 Khanh talk contribs created page Transversal lines (Created page with "== Licensing == Content obtained and/or adapted from: * [https://en.wikipedia.org/wiki/Transversal_(geometry)] under a CC BY-SA license")
- 01:24, 12 December 2021 Khanh talk contribs created page Lines & Angles (Created page with " 290px|thumb|The red and blue lines on this graph have the same [[Slope|slope (gradient); the red and green lines have the same y-intercept (c...")
- 01:04, 12 December 2021 Khanh talk contribs created page Classifying Triangles (Created page with "The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of Euclid's Elements. The names used for modern clas...")
- 00:27, 12 December 2021 Khanh talk contribs created page Theorem of Right Triangles (Created page with "==Right triangles== '''Right triangles''' are [[../Triangle|triangle]]s in which one of the interior angles is 90<sup>o</sup>. A 90<sup>o</sup> angle is called a '''right a...")
- 00:03, 12 December 2021 Khanh talk contribs created page Properties of Polygons (Sides, Angles and Diagonals) (Created page with "== Angles== thumb|Winkelsumme-polygon|Partitioning an n-gon into n − 2 triangles Any polygon has as many corners as it has sides. Each corne...")
- 18:53, 11 December 2021 Khanh talk contribs created page Definition of Polygons (Created page with "File:Assorted polygons.svg|Assorted polygons|Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boun...")
- 18:35, 11 December 2021 Khanh talk contribs created page Models and basic operation with decimals (Created page with "=Decimals= '''Decimals''' are basically fractions expressed without a denominator, rather replaced by a ''power of ten'', and then the decimal point is inserted into the numer...")
- 16:59, 11 December 2021 Khanh talk contribs created page Real Numbers (Rational vs. Irrational Numbers) (Created page with "= Rational number = File:Number-systems.svg|thumb|The rational numbers (<math>\mathbb{Q}</math>) are included in the real numbers (<math>\mathbb{R}</math>), while themselves...")
- 16:10, 11 December 2021 Khanh talk contribs created page Multiplication and division of fractions (Created page with "== Multiplying Fractions == Multiplying fractions is very easy. Simply multiply the numerators of the fractions to find the numerator of the answer. Then multiply the denomina...")
- 16:00, 11 December 2021 Khanh talk contribs created page Addition and subtraction of fractions (Created page with "== Adding Fractions == === Adding Fractions With The Same Denominator === In order to add fractions with the same denominator, you only need to add the numerators while keepi...")
- 15:52, 11 December 2021 Khanh talk contribs created page Divisibility Tests (Created page with "Divisibility rules of whole numbers are very useful because they help us to quickly determine if a number can be divided by 2, 3, 4, 5, 9, and 10 without doing long division....")
- 15:00, 11 December 2021 Khanh talk contribs created page Divisibility (Created page with "A '''divisibility rule''' is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by exam...")
- 11:52, 11 December 2021 Khanh talk contribs created page Exponents (Created page with "== Licensing == Content obtained and/or adapted from: * [https://en.wikibooks.org/wiki/Algebra/Exponents Exponents, Wikibooks: Algebra] under a CC BY-SA license * [https://en...")
- 01:51, 11 December 2021 Khanh talk contribs created page LCM & GCD (Created page with "= Least common multiple = File:Symmetrical_5-set_Venn_diagram_LCM_2_3_4_5_7.svg|thumb|250px|A Venn diagram showing the least common multiples of combinations of 2, 3, 4, 5 a...")
- 01:34, 11 December 2021 Khanh talk contribs created page Equivalents Fractions (Created page with "==Equivalent fractions== Multiplying the numerator and denominator of a fraction by the same (non-zero) number results in a fraction that is equivalent to the original fractio...")
- 01:20, 11 December 2021 Khanh talk contribs created page Prime Numbers (Created page with "== Introduction == A prime number (or prime for short) is a natural number that has exactly two divisors: itself and the number 1. Since 1 has only one divisor — itself —...")
- 00:59, 11 December 2021 Khanh talk contribs created page Patterns (Created page with "= Arithmetic sequence = An '''arithmetic progression''' or '''arithmetic sequence''' is a sequence of numbers such that the difference between the consecutive terms is consta...")
- 15:34, 27 November 2021 Khanh talk contribs created page The Cauchy Criterion (Created page with "Recall that a sequence of real numbers <math>(a_n)</math> is said to be a <strong>Cauchy Sequence</strong> if <math>\forall \epsilon > 0</math> there exists an <math>N \in \ma...")
- 15:16, 27 November 2021 Khanh talk contribs created page Limit of a Sequence in the Real Numbers (Created page with "==Definition== Sequences occur frequently in analysis, and they appear in many contexts. While we are all familiar with sequences, it is useful to have a formal definition....")
- 22:53, 21 November 2021 Khanh talk contribs created page Triangle Inequality (Created page with "== Licensing == Content obtained and/or adapted from: * [http://mathonline.wikidot.com/the-triangle-inequality The Triangle Inequality, mathonline.wikidot.com] under a CC BY-...")
- 22:50, 21 November 2021 Khanh talk contribs created page Absolute Value and the Real Line (Created page with "== The Real Line == thumb|right|382x382px|The real line In mathematics, the '''real line''', or '''real number line''' is the line whose points...")
- 22:38, 21 November 2021 Khanh talk contribs created page Differentiation of Vector-valued Functions (Created page with "==Derivative of a three-dimensional vector function== Many vector-valued functions, like scalar-valued functions, can be differentiated by simply differentiating the componen...")
- 22:32, 21 November 2021 Khanh talk contribs created page Subsequences (Created page with " In mathematics, a '''subsequence''' of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order o...")
- 22:23, 21 November 2021 Khanh talk contribs created page The Cauchy Criterion for Convergence (Created page with "Recall that a sequence of real numbers <math>(a_n)</math> is said to be a <strong>Cauchy Sequence</strong> if <math>\forall \epsilon > 0</math> there exists an <math>N \in \ma...")
- 15:34, 21 November 2021 Khanh talk contribs created page Sequences and Their Limits (Created page with "Consider the sequence <math>\left \{ \frac{1}{n} \right \}_{n=1}^{\infty} = \left \{ 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, ... \right \}</math>. As <math>n \to \infty</mat...")
- 14:33, 21 November 2021 Khanh talk contribs created page Monotone Sequences (Created page with "==Monotone Sequences of Real Numbers== We will now look at two new types of sequences, '''increasing sequences''' and '''decreasing sequences'''. <blockquote style="backgroun...")
- 13:40, 19 November 2021 Lila talk contribs created page Abstract Algebra: Groups (Created page with "<p>Recall that an operation <span class="math-inline"><math>\cdot</math></span> on <span class="math-inline"><math>S</math></span> is said to be associative if for all <span c...")
- 01:08, 19 November 2021 Khanh talk contribs created page Functions(The Cartesian Product Definition) (Created page with " File:Cartesian Product qtl1.svg|thumb|Cartesian product <math>\scriptstyle A \times B</math> of the sets <math>\scriptstyle A=\{x,y,z\}</math> and <math>\scriptstyle B=\{1,...")
- 00:27, 19 November 2021 Khanh talk contribs created page Solutions of Linear Systems (Created page with "==Fundamental Solutions to Linear Homogenous Differential Equations== <blockquote style="background: white; border: 1px solid black; padding: 1em;"> :'''Theorem 1:''' Let <m...")
- 23:37, 18 November 2021 Khanh talk contribs created page Determinant (Created page with "== Wronskian Determinants of Two Functions == We are going to look more into second order linear homogenous differential equations, but before we do, we need to first learn a...")
- 08:43, 18 November 2021 Lila talk contribs created page Abstract Algebra: Preliminaries (Created page with "==Natural numbers== ==Integers== ==Division algorithm== ==Congruence modulo m== ==Algebra on <math>\Z_m</math>== ==GCD, LCM, and Bézout's identity== ==Primes== ===Eucli...")
- 00:02, 18 November 2021 Khanh talk contribs created page Linear Dependence of Vectors (Created page with "==Linear Independence and Dependence== <blockquote style="background: white; border: 1px solid black; padding: 1em;"> :'''Definition:''' A set of vectors <math>V = \{ \mathbf...")
- 23:31, 17 November 2021 Khanh talk contribs created page Direct Integration (Created page with "==The Method of Direct Integration== The simplest differential equations to solve are those in the form of <math>\frac{dy}{dt} = f(t)</math>. These differential equations can...")
- 15:44, 17 November 2021 Lila talk contribs created page Bounded Functions (Created page with "Image:Bounded and unbounded functions.svg|right|thumb|A schematic illustration of a bounded function (red) and an unbounded one (blue). Intuitively, the graph of a bounded f...")
- 14:55, 17 November 2021 Lila talk contribs created page Cosets and Lagrange’s Theorem (Created page with "==Left and Right Cosets of Subgroups== <blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Definition:</strong> Let <span class="math-in...")
- 14:39, 17 November 2021 Lila talk contribs created page Linear Independence of Vectors (Created page with "thumb|right|Linearly independent vectors in <math>\R^3</math> File:Vec-dep.png|thumb|right|Linearly dependent vectors in a plane in <math>\R^3.</math>...")
- 13:57, 17 November 2021 Lila talk contribs created page Permutation Groups (Created page with "A '''permutation group''' is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which ar...")
- 11:17, 17 November 2021 Lila talk contribs created page Cyclic Groups (Created page with "A '''cyclic group''' or '''monogenous group''' is a group that is generated by a single element. That is, it is a set of invertible elements with a single associative binary o...")
- 16:13, 16 November 2021 Lila talk contribs created page Groups (Created page with "<p>Recall that an operation <span class="math-inline"><math>\cdot</math></span> on <span class="math-inline"><math>S</math></span> is said to be associative if for all <span c...")
- 14:29, 16 November 2021 Lila talk contribs created page The Integers (Created page with "An '''integer''' (from the Latin ''integer'' meaning "whole"){{efn|''Integer'' 's first literal meaning in Latin is "untouched", from ''in'' ("not...")
- 13:24, 16 November 2021 Lila talk contribs created page Unions and Intersections of Sets (Created page with "thumb|200px|Union of two sets:<br /><math>~A \cup B</math> [[File:Venn 0111 1111.svg|thumb|200px|Union of three sets:<br /><math>~A \cup B \cup C</math>]...")
- 20:54, 13 November 2021 Khanh talk contribs created page Sequences:Subsequences (Created page with "==Subsequence== In mathematics, a '''subsequence''' of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without chang...")
- 20:37, 13 November 2021 Khanh talk contribs created page Separation Properties (Created page with "In topology and related branches of mathematics, '''separated sets''' are pairs of subsets of a given topological space that are related to each other in a certain way: roughl...")
- 17:52, 13 November 2021 Khanh talk contribs created page Totally Bounded Metric Spaces (Created page with "In topology and related branches of mathematics, '''total-boundedness''' is a generalization of compactness for circumstances in which a set is not n...")
- 17:26, 13 November 2021 Khanh talk contribs created page Bases of Open Sets (Created page with "A set <math>S \subseteq \mathbb{R}^n</math> is said to be open if <math>S =\mathrm{int} (S)</math>, that is, for every point <math>\mathbf{a} \in S</math> we have that there e...")
- 16:55, 13 November 2021 Khanh talk contribs created page A Topology Given By A Metric (Created page with "==Metric Space== ===Definition=== A metric space is a Cartesian pair <math>(X,d)</math> where <math>X</math> is a non-empty set and <math>d:X\times X\to[0,\infty)</math>, is a...")
- 15:43, 13 November 2021 Khanh talk contribs created page The Nested Interval Theorem in Higher Dimensions (Created page with "== Nested Intervals == <blockquote style="background: white; border: 1px solid black; padding: 1em;"> :'''Definition:''' A sequence of intervals <math>I_n</math> where <math>...")
- 12:50, 13 November 2021 Khanh talk contribs created page Iterated Integrals and Fubini's Theorem (Created page with "==Resources== * [https://tutorial.math.lamar.edu/classes/calciii/IteratedIntegrals.aspx Iterated Integrals, Paul's Online Notes] == Licensing == Content obtained and/or adap...")
- 12:29, 13 November 2021 Khanh talk contribs created page Lebesque Theorem for Riemann Integrability on the Real Line (Created page with "In mathematics, the '''Lebesgue differentiation theorem''' is a theorem of real analysis, which states that for almost every point, the value of an integrable function is the...")
- 15:52, 12 November 2021 Khanh talk contribs created page The Inverse Function Theorem and the Implicit Function Theorem (Created page with "In this chapter, we want to prove the inverse function theorem (which asserts that if a function has invertible differential at a point, then it is locally invertible itself)...")
- 15:40, 12 November 2021 Khanh talk contribs created page Taylor's Formula in Several Variables (Created page with "Let <math>S \subseteq \mathbb{R}^n</math> be open, <math>\mathbf{x} \in S</math>, and <math>f : S \to \mathbb{R}</math>. If <math>\mathbf{t} \in \mathbb{R}^n</math> then we kn...")
- 14:27, 12 November 2021 Khanh talk contribs created page Mean-Value Theorems for Vector Valued Functions (Created page with "==The Mean Value Theorem for Differentiable Functions from Rn to Rm== Recall that if <math>f</math> is a continuous function on the closed interval <math>[x, y]</math> and di...")
- 20:04, 11 November 2021 Khanh talk contribs created page Rules for Differentiation and Tangent Planes (Created page with "We will now look at a bunch of rules for differentiating vector-valued function, all of which are analogous to that of differentiating real-valued functions. We will not prove...")
- 17:07, 11 November 2021 Khanh talk contribs created page Limits of Sequences in the Euclidean space and the Bolzano-Weierstrass Theorem (Created page with "File:Archimedes pi.svg|350px|right|thumb|alt=diagram of a hexagon and pentagon circumscribed outside a circle|The sequence given by the perimeters of regular ''n''-sided pol...")
- 12:42, 11 November 2021 Khanh talk contribs created page Laplace Transform to Systems of ODEs (Created page with "This is an example to illustrate how Laplace transforms can be used to solve systems of differential equations. Solve the following system. <div style=...")
- 15:05, 10 November 2021 Lila talk contribs created page Divergence Theorem (Created page with "The '''divergence theorem''', also known as '''Gauss's theorem''' or '''Ostrogradsky's theorem''', is a theorem which relates the flux of a vector field through a closed surfa...")
- 14:13, 10 November 2021 Lila talk contribs created page The Hilbert Space L2 and the Hilbert Cube (Created page with "==Definition and illustration of Hilbert Space== ===Motivating example: Euclidean vector space=== One of the most familiar examples of a Hilbert space is the Euclidean vect...")
- 12:51, 10 November 2021 Lila talk contribs created page Surface Integrals (Created page with "A '''surface integral''' is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. G...")
- 12:17, 10 November 2021 Lila talk contribs created page Partial Derivatives and Integrals (Created page with "===Partial Derivatives of Functions from Rn to Rm=== <p>One of the core concepts of multivariable calculus involves the various differentiations of functions from <span class=...")
- 16:07, 9 November 2021 Lila talk contribs created page The Substitution and Composition Theorems (Created page with "== Substitution Theorem e == === Definite integrals === Let {{math|''φ'' : [''a'', ''b''] → ''I''}} be a differentiable function with a continuous derivative, where {{math...")
- 15:44, 9 November 2021 Lila talk contribs created page The Additivity Theorem (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> Let <span class="math-inline"><math> f </math></span> be a real-valued function on the interval...")
- 15:08, 9 November 2021 Lila talk contribs created page Riemann Integrable Functions (Created page with "== Overview == Let {{mvar|f}} be a non-negative real-valued function on the interval {{math|[''a'', ''b'']}}, and let :<math>S = \left \{ (x, y) \, : \ a \leq x \leq b, 0 <...")
- 14:18, 9 November 2021 Lila talk contribs created page The Topology of Higher Dimensions: interior, closure and boundary (Created page with "We are now going to discuss some important classifications of points regarding a subset <span class="math-inline"><math>S</math></span> of <span class="math-inline"><math>\mat...")
- 14:03, 9 November 2021 Lila talk contribs created page Bounded Sets and Bounded Functions in a Metric Space (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Definition:</strong> Let <span class="math-inline"><math>(M, d)</math></span> be a m...")
- 13:20, 9 November 2021 Lila talk contribs created page The Cartiesian Product (Created page with "File:Cartesian Product qtl1.svg|thumb|Cartesian product <math>\scriptstyle A \times B</math> of the sets <math>\scriptstyle A=\{x,y,z\}</math> and <math>\scriptstyle B=\{1,2...")
- 15:36, 8 November 2021 Lila talk contribs created page Compactness in Metric Spaces (Created page with "=== Compact Sets in a Metric Space === <p> If <span class="math-inline"><math>(M, d)</math></span> is a metric space and <span class="math-inline"><math>S \subseteq M</math></...")
- 15:26, 8 November 2021 Lila talk contribs created page Complete Metric Spaces (Created page with "<h1 id="toc0"><span>Complete Metric Spaces</span></h1> <p>Recall that a sequence <span class="math-inline"><math>(x_n)_{n=1}^{\infty}</math></span> in <span class="math-inline...")
- 14:31, 8 November 2021 Lila talk contribs created page Baire's Theorem and Applications (Created page with "<h1 id="toc0"><span>The Baire Category Theorem</span></h1> <blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Lemma 1:</strong> Let <sp...")
- 12:40, 8 November 2021 Lila talk contribs created page Stone-Weierstrass Theorem (Created page with "The '''Weierstrass approximation theorem''' states that every continuous function defined on a closed interval {{math|[''a'', ''b'']}} can be uniformly approximated as closely...")
- 11:53, 8 November 2021 Lila talk contribs created page Separable Metric Spaces (Created page with "===Dense Sets in a Metric Space=== <p>We will now look at a new concept regarding metric spaces known as dense sets which we define below.</p> <blockquote style="background: w...")
- 11:08, 8 November 2021 Lila talk contribs created page Connectedness (Created page with "===Connected and Disconnected Metric Spaces=== <blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Definition:</strong> A metric space...")
- 10:40, 8 November 2021 Lila talk contribs created page Convergent Sequences in Metric Spaces (Created page with "===Limits of Sequences in Metric Spaces=== <p>Recall that if a sequence of real numbers <span class="math-inline"><math>(x_n)_{n=1}^{\infty} = (x_1, x_2, ..., x_n, ...)</math>...")
- 10:11, 8 November 2021 Lila talk contribs created page Open Sets and Closed Sets in Metric Spaces (Created page with "<h1 id="toc0"><span>Open and Closed Sets in Metric Spaces</span></h1> A set <span class="math-inline"><math>S \subseteq \mathbb{R}^n</math></span> is said to be open if <span...")
- 09:27, 8 November 2021 Lila talk contribs created page Suprema, Infima, and the Completeness Property (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Definition:</strong> Let <span class="math-inline"><math>S</math></span> be a set th...")
- 08:50, 8 November 2021 Lila talk contribs created page Bounded sets in Higher Dimensions (Created page with "<h1 id="toc0"><span>Bounded Sets</span></h1> <p>Consider the set <span class="math-inline"><math>\mathbb{N} = \{ 1, 2, 3, ... \}</math></span>. As you might imagine, there is...")
- 15:21, 7 November 2021 Khanh talk contribs created page Properly Divergent Sequences (Created page with "Recall that a sequence <math>(a_n)</math> of real numbers is said to be <strong>convergent</strong> to the real number <math>A</math> if <math>\forall \epsilon > 0</math> ther...")
- 14:18, 7 November 2021 Khanh talk contribs created page Neighborhoods in R (Created page with "<h1 id="toc0">The Real Number Line</h1> <p>One way to represent the real numbers <math>\mathbb{R}</math> is on the real number line as depicted below.</p> File:Real numbe...")
- 14:47, 6 November 2021 Khanh talk contribs created page Cluster Points (Created page with "In mathematics, a '''limit point''' (or '''cluster point''' or '''accumulation point''') of a set <math>S</math> in a topological space <math>X</math> is a point <math>x</math...")
- 07:43, 3 November 2021 Lila talk contribs created page Stokes' Theorem (Created page with "thumb|right|An illustration of Stokes' theorem, with surface {{math|Σ}}, its boundary {{math|∂Σ}} and the normal vector {{mvar|n}}. '''Stok...")
- 07:23, 3 November 2021 Lila talk contribs moved page Subspaces of Rⁿ and Linear Independence to Subspaces of Rn and Linear Independence
- 22:59, 30 October 2021 Khanh talk contribs created page Complex Population Growth and Decay Models (Created page with "==Propotionality== thumb|300x300px|The variable ''y'' is directly proportional to the variable ''x'' with proportionality constant ~0.6. ...")
- 10:25, 29 October 2021 Lila talk contribs created page Power Series Solutions (Created page with "In mathematics, the '''power series method''' is used to seek a power series solution to certain differential equations. In general, such a solution assumes a po...")
- 10:20, 29 October 2021 Lila talk contribs created page Laplace Transform to ODEs (Created page with "In mathematics, the Laplace transform is a powerful integral transform used to switch a function from the time domain to the Laplace transform#s-domain equiv...")
- 17:45, 28 October 2021 Lila talk contribs created page Linear Independence of Functions (Created page with "<p>If we have an <math>n^{\mathrm{th}}</math> order linear homogenous differential equation <math>\frac{d^ny}{dt^n} + p_1(t) \frac{d^{n-1}y}{dt^{n-1}} + ... + p_{n-1}(t) \frac...")
- 17:03, 28 October 2021 Lila talk contribs created page Linear Tranformations (Created page with "http://mathonline.wikidot.com/linear-transformations")
- 16:48, 28 October 2021 Lila talk contribs created page Euclidean Spaces: Algebraic Structure and Inner Product (Created page with "==Licensing== Content obtained and/or adapted from: * [http://mathonline.wikidot.com/euclidean-n-space Euclidean n-Space, mathonline.wikidot.com] under a CC BY-SA license * [h...")
- 16:43, 28 October 2021 Lila talk contribs created page Power Series and Analytic Functions (Created page with "==Power Series== http://mathonline.wikidot.com/power-series == Operations on power series == === Addition and subtraction === When two functions ''f'' and ''g'' are decompos...")
- 16:11, 28 October 2021 Lila talk contribs created page Continuous Vector Functions (Created page with "http://mathonline.wikidot.com/continuity-of-vector-valued-functions")
- 16:06, 28 October 2021 Lila talk contribs created page Limits of Vector Functions (Created page with "http://mathonline.wikidot.com/limits-of-vector-valued-functions")
- 12:32, 27 October 2021 Lila talk contribs created page Uniform Convergence of Series of Functions (Created page with "==Pointwise Convergent and Uniformly Convergent Series of Functions== <p>Recall that a sequence of functions <math>(f_n(x))_{n=1}^{\infty}</math> with common domain <math>X</m...")
- 11:08, 27 October 2021 Lila talk contribs created page Uniform Convergence of Sequences of Functions (Created page with "<td><strong>Definition:</strong> An <strong>Infinite Sequence of Functions</strong> <math>(f_n(x))_{n=1}^{\infty} = (f_1(x), f_2(x), ..., f_n(x), ...)</math> is a sequence of...")
- 15:07, 26 October 2021 Lila talk contribs moved page Variation Of Parameters (2nd Order) to Variation Of Parameters
- 14:37, 26 October 2021 Lila talk contribs moved page Method of Undetermined Coefficients (2nd Order) to Method of Undetermined Coefficients
- 14:24, 26 October 2021 Lila talk contribs created page Method of Undetermined Coefficients (2nd Order) (Created page with "In mathematics, the '''method of undetermined coefficients''' is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and...")
- 13:14, 26 October 2021 Lila talk contribs moved page Lindeloff Theorem to Lindelöf Theorem (Misspelled title)
- 12:50, 26 October 2021 Lila talk contribs created page Lindeloff Theorem (Created page with "<h1 id="toc0">Lindelöf and Countably Compact Topological Spaces</h1> <p>Recall from the <a href="/compactness-of-sets-in-a-topological-space">Compactness of Sets in a Topolog...")
- 12:24, 26 October 2021 Lila talk contribs created page Properties of the Integral (Created page with "==Properties== ===Linearity=== The collection of Riemann-integrable functions on a closed interval {{math|[''a'', ''b'']}} forms a vector space under the operations of ...")
- 16:53, 25 October 2021 Lila talk contribs created page Exact Differential Equations (Created page with "==Definition== Given a simply connected and open subset ''D'' of '''R'''<sup>2</sup> and two functions ''I'' and ''J'' which are continuous on ''D'', an implicit first-order o...")
- 14:28, 25 October 2021 Lila talk contribs created page Metric Spaces (Created page with "In mathematics, a '''metric space''' is a set together with a metric on the set. The metric is a function (math...")
- 14:26, 25 October 2021 Lila talk contribs created page Distance Functions, Metrics (Created page with "thumb|200px|An illustration comparing the [[Taxicab geometry|taxicab metric to the Euclidean metric on the plane: According to the taxicab metr...")
- 14:22, 25 October 2021 Lila talk contribs created page Topological Spaces (Created page with "In mathematics, a '''topological space''' is, roughly speaking, a geometrical space in which ''closeness'' is defined but cannot n...")
- 14:19, 25 October 2021 Lila talk contribs created page Heine-Borel Theorem (Created page with "In real analysis the '''Heine–Borel theorem''', named after Eduard Heine and Émile Borel, states: For a subset ''S'' of Euclidean space '''R'''<sup>''n...")
- 14:05, 25 October 2021 Lila talk contribs created page Algebraic Structure of the Real Numbers (Created page with "In mathematics, a '''real number''' is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity th...")
- 13:58, 25 October 2021 Lila talk contribs created page Closed Subsets in Higher Dimensions (Created page with "In geometry, topology, and related branches of mathematics, a '''closed set''' is a set whose complement is an ...")
- 13:56, 25 October 2021 Lila talk contribs moved page Open Subsets in Higher Dimensions to Open Subsets
- 13:54, 25 October 2021 Lila talk contribs created page Open Subsets in Higher Dimensions (Created page with "right|thumb|Example: The blue [[circle represents the set of points (''x'', ''y'') satisfying {{math|1=''x''<sup>2</sup> + ''y''<sup>2</sup> = ''r...")
- 13:52, 25 October 2021 Lila talk contribs created page Limit Points (or Cluster Points) in Higher Dimensions (Created page with "In mathematics, a '''limit point''' (or '''cluster point''' or '''accumulation point''') of a set <math>S</math> in a topological space <math>X</math...")
- 13:49, 25 October 2021 Lila talk contribs moved page Distance Between Two Points in the Real Numbers to Distance Between Two Points
- 13:47, 25 October 2021 Lila talk contribs created page The Nested Interval Theorem for the Real Numbers (Created page with "thumb|400px|4 members of a sequence of nested intervals In mathematics, a sequence of '''nested intervals''' is understood as a...")
- 13:41, 25 October 2021 Lila talk contribs created page Limit of a sequence in the Real Numbers (Created page with "File:Archimedes pi.svg|350px|right|thumb|alt=diagram of a hexagon and pentagon circumscribed outside a circle|The sequence given by the perimeters of regular ''n''-sided [[p...")
- 13:38, 25 October 2021 Lila talk contribs created page Distance Between Two Points in the Real Numbers (Created page with "thumb|upright=1.35|Using the Pythagorean theorem to compute two-dimensional Euclidean distance In mathematics, the '''Euclidean distance...")
- 13:34, 25 October 2021 Lila talk contribs created page Cauchy-Schwarz Formula (Created page with "The '''Cauchy–Schwarz inequality''' (also called '''Cauchy–Bunyakovsky-Schwarz inequality''')<ref>{{cite web|url=https://mathshistory.st-andrews.ac.uk/Biographies/Schwarz/...")
- 12:19, 25 October 2021 Lila talk contribs created page The Fundamental Theorem (Created page with "The '''fundamental theorem of calculus''' is a theorem that links the concept of differentiating a function (calculating the grad...")
- 11:27, 25 October 2021 Lila talk contribs created page The Darboux Integral (Created page with "In real analysis, a branch of mathematics, the '''Darboux integral''' is constructed using '''Darboux sums''' and is one possible definition of the integral of a [...")
- 11:23, 25 October 2021 Lila talk contribs created page The Riemann Integral (Created page with "== Licensing == Content obtained and/or adapted from: * [http://mathonline.wikidot.com/riemann-stieltjes-integrals Riemann-Stieltjes Integrals from mathonline.wikidot.com] un...")
- 13:07, 22 October 2021 Lila talk contribs created page Relative Extrema and Convex Functions (Created page with " http://mathonline.wikidot.com/convex-and-concave-functions")
- 13:06, 22 October 2021 Lila talk contribs created page Newton's Method (Created page with "In numerical analysis, '''Newton's method''', also known as the '''Newton–Raphson method''', named after Isaac Newton and Joseph Raphson, is a root-finding alg...")
- 09:29, 22 October 2021 Lila talk contribs created page Linear Differential Equations (Created page with "In mathematics, a '''linear differential equation''' is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives,...")
- 09:08, 22 October 2021 Lila talk contribs created page Homogeneous Differential Equations (Created page with "A differential equation can be '''homogeneous''' in either of two respects. A first order differential equation is said to be homogeneous if it may be written :<math...")
- 16:11, 21 October 2021 Khanh talk contribs created page Variation Of Parameters (2nd Order) (Created page with "In mathematics, '''variation of parameters''', also known as '''variation of constants''', is a general method to solve inhomogeneous linear ordinary differential equations....")
- 15:11, 21 October 2021 Lila talk contribs created page The Limit Theorems for Functions (Created page with "<h1 id="toc0">The Uniqueness of Limits of a Function Theorem</h1> <p>Recall from <a href="/the-limit-of-a-function">The Limit of a Function</a> page that for a function <math>...")
- 14:52, 20 October 2021 Lila talk contribs created page VariationOfParameters2Ord (Created page with "In mathematics, '''variation of parameters''', also known as '''variation of constants''', is a general method to solve inhomogeneous differential equation|inhomogeneous...")
- 14:35, 20 October 2021 Lila talk contribs created page Extrema of a Function (Created page with "thumb|Local and global maxima and minima for cos(3π''x'')/''x'', 0.1≤'' x ''≤1.1 In mathematical analysis, the '''maxima''' and...")
- 14:24, 20 October 2021 Lila talk contribs created page Derivatives of Functions with Inverses (Created page with "File:Umkehrregel 2.png|thumb|right|250px|Rule:<br><math>{\color{CornflowerBlue}{f'}}(x) = \frac{1}{{\color{Salmon}{(f^{-1})'}}({\color{Blue}{f}}(x))}</math><br><br>Example f...")
- 14:22, 20 October 2021 Lila talk contribs created page The Derivative (Created page with "thumb|The [[graph of a function, drawn in black, and a tangent line to that graph, drawn in red. The slope of the tangent line is equa...")
- 14:04, 20 October 2021 Lila talk contribs created page Neighborhoods in 𝐑 (Created page with "<h1 id="toc0">The Real Number Line</h1> <p>One way to represent the real numbers <math>\mathbb{R}</math> is on the real number line as depicted below.</p> <div class="image-co...")
- 13:25, 20 October 2021 Lila talk contribs created page Real Function Limits:Infinite (Created page with "==Informal Infinite Limits== Another kind of limit involves looking at what happens to <math>f(x)</math> as <math>x</math> gets very big. For example, consider the function <m...")
- 13:19, 20 October 2021 Lila talk contribs created page Real Function Limits:One-Sided (Created page with "In calculus, a '''one-sided limit''' is either of the two limits of a function ''f''(''x'') of a real v...")
- 13:07, 20 October 2021 Lila talk contribs created page Divergence Criteria (Created page with "<h1 id="toc0">The Divergence Criteria for Sequences</h1> <p>Thus far we have looked at criteria for sequences to be convergent. We will now begin to look at some criteria whic...")
- 12:55, 20 October 2021 Lila talk contribs created page Monotone Functions (Created page with "right|thumb|Figure 1. A monotonically non-decreasing function. Image:Monotonicity example2.svg|right|thumb|Figure 2. A monotonically non-...")
- 12:24, 20 October 2021 Lila talk contribs created page The Continuous Extension Theorem (Created page with " ==Resources== * [http://mathonline.wikidot.com/the-continuous-extension-theorem The Continuous Extension Theorem], mathonline.wikidot.com")
- 11:22, 20 October 2021 Lila talk contribs created page Uniform Continuity (Created page with "File:Continuity and uniform continuity 2.gif|thumb|upright=1.5|The graph of <math>f(x)=\tfrac1x</math> escapes the top and/or bottom of the <math>\text{height}\times \text{w...")
- 11:20, 20 October 2021 Lila talk contribs created page Lipschitz Functions (Created page with "File:Lipschitz Visualisierung.gif|thumb|right|For a Lipschitz continuous function, there exists a double cone (white) whose origin can be moved along the graph so that the w...")
- 10:35, 20 October 2021 Lila talk contribs created page Sequences:Tails (Created page with "<h1 id="toc0">The Tail of a Sequence of Real Numbers</h1> <p>We will now look at an important aspect of a sequence known as the tail of a sequence.</p> <table class="wiki-cont...")
- 09:56, 20 October 2021 Lila talk contribs created page Sequences:Limits (Created page with "In mathematics, the '''limit of a sequence''' is the value that the terms of a sequence "tend to", and is often denoted using the <math>\lim</math> symbol (e.g., <math...")
- 09:16, 20 October 2021 Lila talk contribs created page Real Function Limits:Sequential Criterion (Created page with "The Sequential Criterion for a Limit of a Function We will now look at a very important theorem known as The Sequential Criterion for a Limit which merges the concept of the l...")
- 19:09, 19 October 2021 Lila talk contribs created page Cluster Points in 𝐑 (Created page with "In mathematics, a '''limit point''' (or '''cluster point''' or '''accumulation point''') of a set <math>S</math> in a topological space <math>X</math...")
- 18:55, 19 October 2021 Lila talk contribs created page Real Numbers:Bounded Subsets (Created page with "Image:Bounded unbounded.svg|right|thumb|An artist's impression of a bounded set (top) and of an unbounded set (bottom). The set at the bottom continues forever towards the r...")
- 18:28, 19 October 2021 Lila talk contribs created page Functions:Operations (Created page with "===Operations=== Functions obey many of the same operations as normal numbers. However, one key difference is the domain of the function, which may change depending on the ope...")
- 15:43, 19 October 2021 Khanh talk contribs created page Inverse Laplace Transform (Created page with " In mathematics, the '''inverse Laplace transform''' of a function ''F''(''s'') is the piecewise-continuous and exponentially-restricted real function ''f''(''t'') which has t...")
- 15:26, 19 October 2021 Lila talk contribs created page Real Numbers:Irrational (Created page with "right|thumb|240px|The number [[Square root of 2|{{radic|2}} is irrational.]] In mathematics, the '''irrational numbers''' (from in-...")
- 15:13, 19 October 2021 Lila talk contribs created page Real Numbers:Rational (Created page with "thumb|The rational numbers (<math>\mathbb{Q}</math>) are included in the [[real numbers (<math>\mathbb{R}</math>), while themselves including the [...")
- 14:50, 19 October 2021 Lila talk contribs created page Real Numbers:Suprema and Infima (Created page with "Image:Infimum illustration.svg|thumb|right|250px|A set <math>P</math> of real numbers (hollow and filled circles), a subset <math>S</math> of <math>P</math> (filled circles)...")
- 13:12, 19 October 2021 Lila talk contribs created page Real Numbers:Absolute Value (Created page with "== Absolute Values == ''Absolute Values'' represented using two vertical bars, <math>\vert</math>, are common in Algebra. They are meant to signify the number's distance from...")
- 13:01, 19 October 2021 Lila talk contribs created page Real Numbers:Inequalities (Created page with "== Definition of Inequalities == As opposed to an equation, an '''inequality''' is an expression that states that two quantities are unequal or not equivalent to one another....")
- 12:42, 19 October 2021 Lila talk contribs created page Sigma Notation (Created page with "Summation notation allows an expression that contains a sum to be expressed in a simple, compact manner. The uppercase Greek letter sigma, Σ, is used to denote the sum o...")
- 11:40, 19 October 2021 Lila talk contribs created page Extreme values on closed and bounded domains (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> '''Extreme Value Theorem:''' If ''f'' is a continuous function and closed on the interval [<mat...")