All public logs

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 50 | older 50) (20 | 50 | 100 | 250 | 500)

• 13:34, 15 October 2021 Lila talk contribs created page Techniques for Finding Derivatives (Created page with "== Techniques of Differentiation == <p> The definition of a derivative, <math>f'(x)=\lim_{{\Delta}x\rightarrow 0} \frac{f(x+{\Delta}x)-f(x)}{{\Delta}x}</math> is not the only...")
• 09:34, 15 October 2021 Lila talk contribs created page Multiple Integrals (Created page with "thumb|right|Integral as area between two curves. File:Volume under surface.png|right|thumb|Double integral as volume under a surface {{math...")
• 15:57, 14 October 2021 Lila talk contribs created page Cauchy Problem (Created page with "A '''Cauchy problem''' in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain...")
• 15:11, 14 October 2021 Lila talk contribs created page Theorem:Bolzano-Weierstrass (Created page with "===Theorem (Bolzano—Weierstrass)=== <blockquote style="background: white; border: 1px solid black; padding: 1em;">Every bounded sequence of real numbers contains a conve...")
• 14:52, 14 October 2021 Lila talk contribs created page Continuous Functions (Created page with "'''Continuity''' marks a new classification of functions, especially prominent when the theorems explained later on in this page will be put to use. However, if one is reading...")
• 14:14, 14 October 2021 Lila talk contribs moved page Cardinality:𝐍 to Cardinality of important sets (Too specific)
• 13:59, 14 October 2021 Lila talk contribs created page Cardinality:𝐍 (Created page with "Two important generalizations of natural numbers arise from the two uses of counting and ordering: cardinal numbers and ordinal numbers. * A natural number can be used to expr...")
• 13:19, 13 October 2021 Lila talk contribs created page Sets:Uncountable (Created page with "In mathematics, an '''uncountable set''' (or '''uncountably infinite set''')<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Uncountably Infinite|url=https://m...")
• 13:01, 13 October 2021 Lila talk contribs created page Sets:Countable (Created page with "In mathematics, a '''countable set''' is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A countable set is either a finite...")
• 09:59, 13 October 2021 Lila talk contribs created page Real Numbers:Sequences (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....")
• 09:35, 13 October 2021 Lila talk contribs created page Functions:Restriction (Created page with "thumb|The function ''x''² with domain '''R''' does not have an [[inverse function. If we restrict ''x''² to the non-neg...")
• 14:49, 12 October 2021 Lila talk contribs created page The Least-squares Solution (Created page with "'''Ordinary least squares''' ('''OLS''') is a type of linear least squares method for estimating the unknown parameters in a linear regression model. OLS chooses the parameter...")
• 13:51, 12 October 2021 Lila talk contribs created page Recursion (Created page with "==Recursion in mathematics== thumb|250px|The [[Sierpinski triangle—a confined recursion of triangles that form a fractal]] ===Recursively d...")
• 13:03, 12 October 2021 Lila talk contribs created page Natural Numbers:Well-Ordering (Created page with "In mathematics, the well-ordering principle states that every non-empty set of positive integers contains a least element.[1] In other words, the set of positive integers is w...")
• 09:08, 12 October 2021 Lila talk contribs created page Functions:Forward Image (Created page with "File:Codomain2.SVG|thumb|upright=1.5|<math>f</math> is a function from domain <math>X</math> to codomain <math>Y.</math> The yellow oval inside <math>Y</math> is the image o...")
• 08:48, 12 October 2021 Lila talk contribs created page Real Numbers:Algebraic Properties (Created page with "===Some simple results=== At this point there are a large number of very simple results we can deduce about these operations from the axioms. Some of these follow, and some o...")
• 08:44, 12 October 2021 Lila talk contribs created page Real Numbers (Created page with "==Why we need the real numbers== This is a good juncture to justify the subject of real analysis, which essentially reduces to justifying the necessity of studying <math>\R</m...")
• 14:11, 8 October 2021 Lila talk contribs created page The Geometric Interpretation of the Determinant (Created page with "This parallelogram picture <center> x200px </center> is familiar from the construction of the sum of the two vectors. One way to compute the...")
• 14:02, 8 October 2021 Lila talk contribs created page Diagonalization of Matrices (Created page with "The prior subsection defines the relation of similarity and shows that, although similar matrices are necessarily matrix equivalent, the converse does not hold. Some matrix-eq...")
• 13:40, 8 October 2021 Lila talk contribs created page Orthonormal Bases and the Gram-Schmidt Process (Created page with "The prior subsection suggests that projecting onto the line spanned by <math> \vec{s} </math> decomposes a vector <math>\vec{v}</math> into two parts <center> <TABLE border=0p...")
• 13:12, 8 October 2021 Lila talk contribs created page The Dimension of a Vector Space (Created page with "In the prior subsection we defined the basis of a vector space, and we saw that a space can have many different bases. For example, following the definition of a basis, we saw...")
• 12:39, 8 October 2021 Lila talk contribs created page The Column Space and Nullspace of a Linear Transformation (Created page with "Isomorphisms and homomorphisms both preserve structure. The difference is that homomorphisms needn't be onto and needn't be one-to-one. This means that homomorphisms are a mor...")
• 16:37, 7 October 2021 Lila talk contribs created page Applications of Derivatives (Created page with " ==Resources== * [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Derivative%20Formulas/Presentation3b,4,5_Limits%20&%20Derivative%20Formulas.pptx Limits & Derivative Formulas...")
• 16:13, 2 October 2021 Lila talk contribs created page Piecewise Linear Function (Created page with "rightA piecewise function is a function that is given by different expressions on different intervals. The graph of <math>f(x) = \begin{cases} x^2, &...")
• 15:51, 2 October 2021 Lila talk contribs created page Sets:Cardinality (Created page with "==Infinite Sets and Cardinality== '''The Size of a Finite Set''' When deciding how large finite sets are, we generally count the number of elements in the set, and say two se...")
• 13:10, 1 October 2021 Lila talk contribs created page Two-dimensional coordinate systems (Created page with "==Two-Dimensional Vectors== ===Introduction=== In most mathematics courses up until this point, we deal with '''scalars'''. These are quantities which only need one number to...")
• 11:33, 1 October 2021 Lila talk contribs created page Proofs:Induction (Created page with "The beauty of induction is that it allows a theorem to be proven true where an infinite number of cases exist without exploring each case individually. Induction is analogous...")
• 11:21, 1 October 2021 Lila talk contribs created page Natural Numbers:Postulates (Created page with "==Peano's Axioms for the Natural Numbers== # 1 is a natural number. # For every natural number <math> n </math>, the successor to <math> n </math> (<math> n + 1 </math>) is al...")
• 10:51, 1 October 2021 Lila talk contribs created page Sets:Families (Created page with "A set of sets is usually referred to as a ''family'' or ''collection'' of sets. Often, families of sets are written with either a script or [http://en.wikipedia.org/wiki/Frakt...")
• 10:41, 1 October 2021 Lila talk contribs created page The First Derivative Test (Created page with "== The First Derivative Test == <p> The definition of a derivatives tells us that a derivative is the slope of the tangent line at a point on the function. </p> <p> Derivative...")
• 15:59, 30 September 2021 Lila talk contribs created page Mathematical Error (Created page with "At the time of writing this, the 'population clock' run by the USA states that there are 316,356,429 people living in the USA. However, many sources will say that the populati...")
• 16:52, 29 September 2021 Lila talk contribs created page Functions as Relations (Created page with "== Introduction == This article examines the concepts of a ''function'' and a ''relation''. A '''''relation''''' is any association or link between elements of one set, call...")
• 13:37, 29 September 2021 Lila talk contribs created page Subspaces of Rⁿ and Linear Independence (Created page with "One of the examples that led us to introduce the idea of a vector space was the solution set of a homogeneous system. For instance, we've seen in Linear Algebra/Definition a...")
• 12:59, 29 September 2021 Lila talk contribs created page Introduction to Linear Transformations (Created page with "A '''linear transformation''' is an important concept in mathematics because many real world phenomena can be approximated by linear models. Unlike a linear function, a line...")
• 12:58, 29 September 2021 Lila talk contribs created page The Inverse of a Linear Transformation (Created page with "A '''linear transformation''' is an important concept in mathematics because many real world phenomena can be approximated by linear models. Unlike a linear function, a line...")
• 12:36, 29 September 2021 Lila talk contribs created page Introduction to Vector Spaces (Created page with "A '''vector space''' (over <math>\R</math>) consists of a set <math>V</math> along with two operations "<math>+</math>" and "<math>\cdot</math>" subject to these conditions....")
• 14:31, 28 September 2021 Lila talk contribs created page Proofs:Quantifiers (Created page with "==Proving a statement with a universal quantifier== To prove a statement of the form :For all <math>x</math>, <math>P(x)</math> first ask the reader to pick an arbitrary const...")
• 14:11, 28 September 2021 Lila talk contribs created page Series (Created page with "Frequently in analysis it is useful to consider the sum of infinitely many numbers. So for some sequence of numbers (''a''_''n'') we may want to consider expression...")
• 09:54, 28 September 2021 Lila talk contribs created page Writing Mathematics (Created page with "== Parts of a Theorem == A [https://en.wikipedia.org/wiki/Theorem theorem] is a ''proven statement'' that was constructed using previously proven statements, such as theorems,...")
• 15:28, 27 September 2021 Lila talk contribs created page Equivalence Relations (Created page with "We have seen that certain common relations such as "=", and congruence (which we will deal with in the next section) obey some of these rules above. The relations we will deal...")
• 15:24, 27 September 2021 Lila talk contribs created page Relations (Created page with "== Introduction == This article examines the concepts of a ''function'' and a ''relation''. A '''''relation''''' is any association or link between elements of one set, call...")
• 14:44, 27 September 2021 Lila talk contribs created page Functions:Bijective (Created page with "A function is bijective if it is both injective and surjective. That is, a bijective function maps each element of the domain to a distinct element in the codomain, and every...")
• 14:37, 27 September 2021 Lila talk contribs created page Functions:Surjective (Created page with "A function is surjective, or "onto", if for all <math> b\in B </math>, there exists at least one <math> a\in A </math> such that <math> f(a) = b </math>; that is, every elemen...")
• 13:57, 27 September 2021 Lila talk contribs created page Functions:Injective (Created page with "A function <math> f: A\to B </math> is injective, or "one-to-one", if for all <math> a_1, a_2\in A </math>, <math> a_1 \neq a_2 </math> implies that <math> f(a_1) \neq f(a_2)...")
• 12:01, 27 September 2021 Lila talk contribs created page Functions:Definition (Created page with "A function (or "mapping") is a relationship between two sets <math> A </math> and <math> B </math> that maps each input <math> a\in A </math> to exactly one output <math> b\in...")
• 12:44, 26 September 2021 Lila talk contribs created page Sets:Operations (Created page with "==Definitions== The two main set operations that we deal with are union and intersection. The union of two sets <math> A </math> and <math> B </math> is defined as <math> A \c...")
• 10:20, 26 September 2021 Lila talk contribs created page Sets:Definitions (Created page with "==Definitions== A set is any collection of objects. The objects in a set are called elements. For example, <math> \N = {1, 2, 3, ....} </math> is the set of all natural number...")
• 14:21, 24 September 2021 Lila talk contribs created page Eigenvalues and Eigenvectors (Created page with "In linear algebra, an eigenvector of a matrix is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding e...")
• 14:03, 24 September 2021 Lila talk contribs created page MAT3223 (Created page with "MAT 3223. Complex Variables. (3-0) 3 Credit Hours. Prerequisites: MAT 2214 and MAT 3213. An introduction to complex variables, including elementary functions, line integrals,...")
• 13:51, 24 September 2021 Lila talk contribs created page Logical Implication (Created page with "A logical implication is a relationship between two statements. If a statement Q is always true when another statement P is true, then we say that "P implies Q", which is deno...")

(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)