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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).

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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 90o. A 90o 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 Cauchy Sequence 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 Cauchy Sequence 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 "Recall that an operation <math>\cdot</math> on <math>S</math> 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>Definition: 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 "Recall that an operation <math>\cdot</math> on <math>S</math> 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: <math>~A \cup B</math> [[File:Venn 0111 1111.svg|thumb|200px|Union of three sets: <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>...")

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