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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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• 12:42, 15 October 2021 Khanh talk contribs created page Proportionality vs. Linearity (Created page with " thumb|300x300px|The variable ''y'' is directly proportional to the variable ''x'' with proportionality constant ~0.6. File:Inverse propo...")
• 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...")
• 19:42, 14 October 2021 Khanh talk contribs created page Optimization Applications (Created page with " ==Introduction== Optimization is one of the uses of calculus in the real world. Perhaps we are a pizza parlor and wish to maximize profit. Perhaps we have a flat piece of car...")
• 16:10, 14 October 2021 Khanh talk contribs created page Absolute change (additive reasoning) & Relative change (multiplicative reasoning) (Created page with "=Measuring Errors= In this lesson we will learn how to quantify errors. Learning objectives * identify true and relative true errors * identify approximate and relative appro...")
• 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...")
• 15:20, 14 October 2021 Khanh talk contribs created page Continuous Growth (Created page with "File:Exponential.svg|thumb|300px|right|The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth. {{legend|green|Exponential g...")
• 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...")
• 00:36, 12 October 2021 Khanh talk contribs created page Univariate, Bivariate, Correlation and Causation (Created page with "==Univariate Data== In mathematics, a '''univariate''' object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one...")
• 00:26, 12 October 2021 Khanh talk contribs created page Geometric interpretation of interpolation (Created page with "In the mathematical field of numerical analysis, '''interpolation''' is a type of estimation, a method of constructing (finding) new data points based on the range of a discre...")
• 22:26, 10 October 2021 Khanh talk contribs created page Depreciation (Created page with "thumb|380px|An asset depreciation at 15% per year over 20 years In accountancy, '''depreciation''' refers to two aspects of the same concept: fir...")
• 21:41, 10 October 2021 Khanh talk contribs created page Regression (Created page with "==Regression== Regression analysis is the process of building a model of the relationship between variables in the form of mathematical equations. The general purpose is to e...")
• 21:24, 10 October 2021 Khanh talk contribs created page Simple and Compound Interest (Linear and Exponential Models) (Created page with "'''Interest''', in finance and economics, is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the princ...")
• 01:17, 9 October 2021 Khanh talk contribs created page Proportional reasoning (Created page with "== Vocabulary == '''Ratio:''' The comparison of two numbers. '''Reciprocal:''' The multiplicative inverse of a number -- when the numerator and denominator of a fraction are...")
• 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...")
• 17:10, 6 October 2021 Khanh talk contribs created page Debt-to-income (DTI) ratios (Created page with "In the consumer mortgage industry, '''debt-to-income ratio''' (often abbreviated '''DTI''') is the percentage of a consumer's monthly gross income that goes toward paying debt...")
• 20:20, 3 October 2021 Khanh talk contribs created page Sets:Finite (Created page with "In mathematics (particularly set theory), a '''finite set''' is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle cou...")
• 19:48, 3 October 2021 Khanh talk contribs created page Functions:Composition (Created page with "In mathematics, '''function composition''' is an operation that takes two functions {{math|''f''}} and {{math|''g''}} and produces a function {{math|''h''}} such that {{math|1...")
• 16:50, 3 October 2021 Khanh talk contribs created page Functions:Inverse Image (Created page with "The '''inverse image''' (or '''preimage''') of a given subset <math>B</math> of the codomain of <math>f,</math> is the set of all elements of the domain that map to the member...")
• 16:44, 3 October 2021 Khanh talk contribs created page Functions:Inverses (Created page with " Image:Inverse Function.png|thumb|right|A function {{mvar|f}} and its inverse {{math|''f''⁻¹}}. Because {{mvar|f}} maps {{mvar|a}} to 3, the inverse {{math|'...")
• 15:01, 3 October 2021 Khanh talk contribs created page Introduction to Determinants (Created page with "The determinant is a function which associates to a square matrix an element of the field on which it is defined (commonly the real or complex numbers). The determinant is req...")
• 14:49, 3 October 2021 Khanh talk contribs created page Dot Products and Orthogonality (Created page with "We first consider orthogonal projection onto a line. To orthogonally project a vector <math> \vec{v} </math> onto a line <math>\ell</math>, mark the point on the line at which...")
• 14:27, 3 October 2021 Khanh talk contribs created page Mathematical (Linear) relationships (Created page with "==Linear Relationship== We are going to start by looking at simple functions called '''linear equations'''. When none of the instances of x and y in the algebraic expressio...")
• 14:16, 3 October 2021 Khanh talk contribs created page The Sine Function (Created page with "==Sine and Cosine Graphs== And here in this graph, the colors we've chosen to draw the waves in have no relation to the frequency. Both waves have the same frequency, but we'v...")
• 13:52, 3 October 2021 Khanh talk contribs created page Ratios and percentages (Created page with "==Ratio== In mathematics, a '''ratio''' indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then t...")
• 13:29, 3 October 2021 Khanh talk contribs created page Graphical Display (Created page with "thumb|A pie chart showing the composition of the 38th Parliament of Canada. A '''chart''' is a graphical representation for data v...")
• 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...")

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