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• Operations on functions
  [[image:boys and balls.png| center]] [[image:boys and balls -- union.png| center]]
  142 KB (23,566 words) - 02:01, 23 February 2019
• Precalculus
  [[image:road and nothing.png| center]] [[image:coordinate system dim 1.png| center]]
  100 KB (16,148 words) - 20:04, 18 January 2017
• Vector and complex variables
  [[image:solution of linear system.png| center]] [[image:solution of linear system 2.png| center]]
  113 KB (18,750 words) - 02:33, 10 December 2018
• The derivative
  [[Image:light bounce off a curved mirror.png| center]] [[image:secant.png| center]]
  75 KB (13,000 words) - 15:12, 7 December 2018
• Several variables
  [[image:constant speed.png| center]] [[image:constant acceleration.png| center]]
  76 KB (13,017 words) - 20:26, 23 February 2019
• Limits and continuity
  [[image:limits of functions.png| center]] [[image:lim f(x) via lim a_n.png| center]]
  107 KB (18,743 words) - 17:00, 10 February 2019
• Functions in higher dimensions
  [[image:time-location-altitude.png| center]] [[image:composition -- time-location-altitude.png| center]]
  113 KB (19,680 words) - 00:08, 23 February 2019
• Classes of functions
  [[image:boys and balls -- constant.png| center]] [[image:constant map.png| center]]
  143 KB (24,052 words) - 13:11, 23 February 2019
• Differentiation
  [[image:Sum Rule for differentials.png| center]] [[image:Constant Multiple Rule for differentials.png| center]]
  82 KB (14,116 words) - 19:50, 6 December 2018
• Precalculus exercises
  [[image:parabola on grid.png| center]] [[image:area between parabola and horizontal line.png| center]]
  17 KB (2,933 words) - 19:37, 30 July 2018
• Topology
  ...y is the science of spatial properties that are preserved under continuous transformations.'' To elaborate a bit: you can bend, stretch, and shrink but '''not''' tear <!--100-->[[image:topology-algebra-geometry 1.png|center]]
  20 KB (3,407 words) - 21:46, 30 November 2015
• Continuous functions
  <!--200-->[[Image:continuous vs discontinuous.png|center]] <!--200-->[[Image:continuous function.png|center]]
  42 KB (7,138 words) - 19:08, 28 November 2015
• Transformations
  ==Functions as transformations== [[image:solution of linear system.png| center]]
  46 KB (7,625 words) - 13:08, 26 February 2018
• Homotopy
  [[image:circles.png|center]] <!--150-->[[image:circle homotopy type.png|center]]
  46 KB (7,846 words) - 02:47, 30 November 2015
• Maps of graphs
  ...<!--\index{Topology}--> would be incomplete without considering continuous transformations of objects, also known as maps<!--\index{maps}-->. <!--250-->[[image:components and holes under maps.png|center]]
  29 KB (5,042 words) - 17:57, 28 November 2015
• Calculus Illustrated
  [[image:Calculus Illustrated.png|right]] 16 The image: the range of values of a function
  16 KB (1,933 words) - 19:50, 28 June 2021
• Topology of graphs
  *develop further methods for studying transformations of these structures. [[Image:graph examples.png|center]]
  25 KB (4,214 words) - 16:08, 28 November 2015
• Robustness of geometry
  ...and objects are large. So the question is, what changes to the image will produce "small" changes to the output of analysis, especially [[Measur <p>Let’s consider a very simple example. Suppose we have an image containing a 1x1 black square on white background. Suppose also that the re
  4 KB (604 words) - 16:35, 12 March 2010
• Robustness of topology
  ...dding a single pixel shouldn't dramatically change the [[topology]] of the image. But it does! The example on the right shows that adding the red pixel merg [[Image:Adding_whole_pixel.JPG|center]]
  5 KB (784 words) - 13:28, 28 August 2015
• Object recognition
  ...y different from "image recognition". The latter is essentially [[image-to-image search]]. ...a few examples: Numenta (below) and others that try object recognition for image search:
  3 KB (520 words) - 22:59, 6 September 2010
• Precision and recall
  <p>[[Pixcavator image search]] searches for images based on similarity, a potential application o ...nly used in information retrieval. Below, we just replace “document” with “image”.</p>
  4 KB (669 words) - 03:34, 6 September 2010
• Mathematics of computer vision: course
  This is an introduction into the mathematics of computer vision and digital image analysis: [[topology]] and [[geometry]]. (For a more advanced approach see [[image:Topology_graph.jpg|right|400px]]
  3 KB (436 words) - 15:05, 24 October 2015
• MATLAB
  ==Example of image analysis== [[Image:CellsMATLABoriginal.jpg|300px]] [[Image:CellsMATLAB.jpg|330px]][[Image:CellsMATLABoriginal_2000_60.jpg|300px]]
  4 KB (548 words) - 14:55, 9 October 2010
• The topology of data
  [[Image:Torus.JPG|thumb|right|300px|Betti Numbers: B₀ = 1 (parts), B<sub We will compute the spacial properties that are preserved under topological transformations, i.e. you can bend, stretch, or shrink but not tear or glue. We determine t
  9 KB (1,431 words) - 16:57, 20 February 2011
• Modeling with discrete exterior calculus
  ...ed like this is rather difficult. It is obvious that simply looking at the image, one may determine how circular the object is, but getting a computer to lo [[image:ExcelFail.jpg]]
  31 KB (5,254 words) - 17:57, 21 July 2012
• Elementary Linear Algebra -- Spring 2018 -- final exam
  ...rnel of a linear operator. Find the image and the kernel for the following transformations of the plane: (a) rotation around the origin, (b) flip about the diagonal,
  2 KB (351 words) - 20:49, 30 April 2018
• Elementary Linear Algebra -- Spring 2018
  [[image:no cellphones.png|right]] ...tems of linear equations, matrices and determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications. PR: ACT Math 27 or MTH132
  4 KB (573 words) - 13:07, 7 April 2018
• Elementary Linear Algebra -- Spring 2019
  [[image:no cellphones.png|right]] ...tems of linear equations, matrices and determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications. PR: ACT Math 27 or MTH132
  3 KB (321 words) - 21:06, 19 February 2019