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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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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...")
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...")
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>]...")
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=== 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 <math> f </math> 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 <math>S</math> of <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>Definition: Let <math>(M, d)</math> 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 === If <math>(M, d)</math> is a metric space and <math>S \subseteq M</math></...")
15:26, 8 November 2021 Lila talk contribs created page Complete Metric Spaces (Created page with "<h1 id="toc0">Complete Metric Spaces</h1> Recall that a sequence <math>(x_n)_{n=1}^{\infty}</math> 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">The Baire Category Theorem</h1> <blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td>Lemma 1: 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=== We will now look at a new concept regarding metric spaces known as dense sets which we define below. <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>Definition: 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=== Recall that if a sequence of real numbers <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">Open and Closed Sets in Metric Spaces</h1> A set <math>S \subseteq \mathbb{R}^n</math> 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>Definition: Let <math>S</math> 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">Bounded Sets</h1> Consider the set <math>\mathbb{N} = \{ 1, 2, 3, ... \}</math>. As you might imagine, there is...")
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
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 "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== 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>Definition: An Infinite Sequence of Functions <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> 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'''2 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...")

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