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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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• 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^o. A 90^o 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...")
• 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...")
• 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...")
• 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=...")
• 15:21, 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...")
• 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. ...")

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