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• Notation
  *$A^n:=\{(x_1,...,x_n):x_i\in A\} \quad$ the $n$th power of set $A$; ...X:A \hookrightarrow X \quad$ the inclusion function of subset $A\subset X$ of set $X$ into $X$;
  8 KB (1,519 words) - 16:30, 1 December 2015
• College Algebra -- Fall 2016
  ...ynomial, rational, exponential, and logarithmic functions. Graphs, systems of equations and inequalities, sequences. (PR: Math ACT 21 or above) *Prerequisites: solid algebra skills, some knowledge of Cartesian coordinates, familiarity with basic functions
  10 KB (1,078 words) - 19:07, 16 December 2016
• Links
  *[[Calculus as a part of topology]] *[[Multilinear algebra]]
  6 KB (998 words) - 12:40, 31 August 2015
• Calculus I -- Spring 2017
  ...ions of one variable, including the transcendental functions. (PR: MTH ACT of 27 or above, or MTH 130 and 122, or MTH 127 and 122, or MTH 132) This cours *Prerequisites: fluency with algebra, good understanding of functions
  12 KB (1,803 words) - 20:50, 1 May 2017
• Calculus I -- Fall 2016
  ...ions of one variable, including the transcendental functions. (PR: MTH ACT of 27 or above, or MTH 130 and 122, or MTH 127 and 122, or MTH 132) This cours *Prerequisites: fluency with algebra, good understanding of functions
  11 KB (1,671 words) - 23:11, 13 December 2016
• Fantasy math
  I would like to come up with an outline of what undergraduate mathematics curriculum ought to be. I have to ''ignore the reality'' of college education: prerequisites, "service courses", overlapping degree req
  8 KB (1,196 words) - 13:02, 24 August 2015
• Discrete differential forms
  [[Image:graph of function.png|center]] ...ts values at, say, 0, 1, 2, 4, 5... Suppose that the [[derivative]], $f'$, of the function is also sampled:
  10 KB (1,471 words) - 12:50, 12 August 2015
• Calculus by Stewart
  ...rd, there is nothing wrong with the book. The "Early Transcendentals" part of the title has always bugged me though... A preview of calculus.
  6 KB (794 words) - 16:29, 13 August 2017
• Fundamental group
  The ''fundamental group'' of $(X,x_0)$, $\pi _1(X,x_{0})$, is the [[group]] of loops based at $x_{0}$, up to a based [[homotopy]]. We define a product on where $<x>$ stands for the homotopy class of $x$ and $\sigma \cdot \tau$ means "travel along $\sigma$ and then $\tau$".
  10 KB (1,673 words) - 18:23, 2 December 2012
• Applied Calculus -- Spring 2015
  '''MTH 140 - Applied Calculus''' A brief survey of calculus including both differentiation and integration with applications. ...classes of functions, graph these functions, solve equations -- [[College Algebra -- Fall 2014]]
  9 KB (1,141 words) - 16:08, 26 April 2015
• Advanced Topology: exercises
  #List all antiderivatives of $1/x$ and prove, from the definition, that they are continuous. #Show that the set of differential forms is a vector space.
  9 KB (1,487 words) - 18:18, 9 May 2013
• Calculus I -- Fall 2018
  ...ions of one variable, including the transcendental functions. (PR: MTH ACT of 27 or above, or MTH 130 and 122, or MTH 127 and 122, or MTH 132) This cours *Prerequisites: fluency with algebra, good understanding of functions.
  8 KB (1,184 words) - 17:55, 29 October 2018
• Topology of Surfaces by Kinsey
  ...w pictures here. Chapter 10, Miscellany: Good stuff here: the Jordan Curve Theorem, 3-manifolds, etc., but too little time... Chapter 11, Topology and calculu ...ontinuity: continuity under algebraic operations, the [[Intermediate value Theorem]], [[sequences]], etc.''
  5 KB (725 words) - 12:30, 9 September 2016
• Precalculus with Scientific Applications -- Spring 2016
  ...c sections, polar parametric equations, sequences and series, and Binomial Theorem. (PR:Math ACT 24 or above, or C or better in MTH 127 or C or better in MTH *Prerequisites: solid algebra skills, some knowledge of Cartesian coordinates, familiarity with basic functions
  7 KB (890 words) - 16:32, 20 April 2016
• Differential forms and cohomology: course
  <TR> <TD><center>[[Stokes theorem]]</center></TD></TR> ...an extract [[topological]] information about a [[manifold]] from its space of differential forms. It's called [[cohomology]].
  3 KB (354 words) - 20:54, 13 March 2013
• Degree of map
  The degree is initially defined for [[maps]] of [[circle]]s: as the number of times the first circle is wraps around the second. It is also defined this
  2 KB (353 words) - 13:36, 28 August 2015
• Differential forms: course
  We take a more advanced view of [[calculus]]. The approach allows us to study calculus on [[manifold]]s as <TR> <TD><center>[[Stokes theorem]]</center></TD></TR>
  3 KB (421 words) - 14:44, 8 February 2013
• General Stokes Theorem
  ...light of [[Integration of differential forms of degree 0 and 1|integration of differential forms]]. It's the same for any [[parametrization]] of $[a,b]$, according to one of the properties.
  4 KB (656 words) - 18:26, 9 November 2012
• Homology of surfaces
  What do we know about the [[homology as a vector space|homology]] of $M$? The $0$th homology $H_0$ is [[properties of homology groups|simple]]:
  5 KB (866 words) - 13:00, 28 August 2015
• Calculus of differential forms: course
  ...It covers the derivative, the integral, differential forms, and a variety of applications. An emphasis is made on the coordinate free, vector analysis. *[[Linear algebra: course|Linear algebra]]
  2 KB (217 words) - 20:25, 10 February 2013

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