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www.wolfram.com/.../tutorialcollection/.../AdvancedAlgebra.pdfIn all the tutorials for complex polynomial system solving, assume that the system has been transformed to this form. Reduce can solve arbitrary complex ... -
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[PDF]Mathematica Tutorial: Constrained Optimization - Wolfram Research
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[PDF]Mathematica Tutorial: Advanced Numerical Integration In Mathematica
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www.wolfram.com/.../tutorialcollection/.../NETLinkUserGuide.pdfWolfram Mathematica® Tutorial Collection .NET/LINK™ ..... The LoadNETAssembly function, described later in this tutorial, is the Mathematica func- tion you use ... -
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... expression. After you've read about the basic ideas underlying Geometry Expressions, try running the Geometry Expressions Tutorials to help you get started. -
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AceGen Tutorials. AceGen Preface. AceGen. © Prof. Dr.Joże Korelc, 2006, 2007, 2008, 2009, 2010. Ravnikova 4, SI - 1000, Ljubljana, Slovenia. E–mail ... -
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Oct 22, 2009 - Hands-on Start with Mathematica Tutorial. Kelvin Mischo, Wolfram Education Group. Modeling Long-Term Care Insurance. Seth Chandler. -
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The MathLink directory contains the VI libraries MLStart.llb and Tutorial.llb .... installed, you can access the tutorials from the AddOns section of the. Mathematica ... -
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The ProPac cD contains a set of tutorial and application notebooks. These include Dynamics.nb and controls.nb which introduce the basic modeling and. -
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Oct 25, 2008 - Tutorials. Homewood. 7:00AM. 7:30AM. 8:00AM. 8:30AM. 9:00AM. 9:30AM. Transcendental Roots. Adam Strzebonski. Data Collections. -
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Jan 18, 2014
Wolfram Mathematica Tutorials
Mathematics And Algorithms (free ebook from Wolfram Tutorials)
http://www.wolfram.com/learningcenter/tutorialcollection/MathematicsAndAlgorithms/MathematicsAndAlgorithms.pdf
Description
Mathematica has the most extensive collection of mathematical functions ever assembled. Often relying on original results and algorithms developed at Wolfram Research over the past two decades, each function supports a full range of symbolic operations, as well as efficient numerical evaluation to arbitrary precision, for all complex values of parameters. Topics covered in this collection include algebraic calculations and manipulation, linear algebra, calculus, series and limits, numerical operations, and mathematical functions.
Table of Contents
Numbers | Algebraic Calculations | Algebraic Manipulation | Manipulating Equations and Inequalities | Linear Algebra | Series, Limits and Residues | Calculus | Numerical Operations on Functions | Numerical Operations on Data | Mathematical Functions
Dec 10, 2013
Nov 17, 2013
EMIS ELibM: Mathematical Collections and Conference Proceedings
http://www.emis.de/proceedings/index.html
- 8th International Conference Words 2011
Prague, Czech Republic, 12-16th September 2011 - Workshop on Finsler Geometry and Its Applications
Debrecen, Hungary, 24–29 May 2009 - Geometry, Integrability and Quantization VIII
Varna, Bulgaria: June 9–14, 2006. - The 26th Winter School Geometry and Physics
Srni, Czech Republic, 14–21 January 2006 - Contemporary geometry and Related Topics
Neda Bokan, Mirjana Djorić, Anatoly T. Fomenko, Zoran Rakić, Bernd Wegner, Julius Wess (eds.), Belgrade, Serbia and Montenegro 26 June–2 July 2005 - The 29th International Conference of the International Group for the Psychology of Mathematics Education
Helen Chick and Jill L. Vincent (eds.), Melbourne, Australia 10–15 July 2005 - Geometry, Integrability and Quantization VII
Varna, Bulgaria: June 2–10, 2005. - The 28th International Conference of the International Group for the Psychology of Mathematics Education
Marit Johnsen Høines and Anne Berit Fuglestad (eds.), Bergen, Norway 14–18 July, 2004 - New Developments in Electronic Publishing
Hans Becker, Kari Stange, Bernd Wegner (eds). Stockholm, Sweden: 25–27 June, 2004 - Geometry, Integrability and Quantization VI
Varna, Bulgaria: June 3–10, 2004. - Geometry, Integrability and Quantization V
Varna, Bulgaria: June 5–12, 2003. - Geometry, Integrability and Quantization IV
Varna, Bulgaria: June 6–15, 2002. - Mathematical Knowledge Management (MKM'2001)
Schloss Hagenberg, Austria: September 24–26, 2001 - Workshop on Special Geometric Structures in String Theory
Dmitri V. Alekseevsky, Vicente Cortés, Chandrashekar Devchand and Antoine Van Proeyen (eds.). Bonn, Germany: 8–11 Sep 2001 - Margarita mathematica en memoria de José Javier (Chicho) Guadalupe Hernández
Luis Español and Juan L. Varona (eds.), Logroño, Spain: 2001 - Geometry, Integrability and Quantization III
Varna, Bulgaria: September 1–10, 2001. - TOPOSYM 2001
Prague, Chech Republic: August 19–25, 2001 - Geometry, Integrability and Quantization II
Varna, Bulgaria: June 7–15, 2000. - AMS Special Session on Nonabsolute Integration
Pat Muldowney and Erik Talvila (eds.). Toronto, Canada: 23–24 Sep 2000 - ALGORITMY 2000
Podbanske, Slovakia: September 10–15, 2000 - Geometry & Applications
Novosibirsk, Russia: March 13–16, 2000 - Steps in Differential Geometry
Debrecen, Hungary: July 25–30, 2000 - Geometry, Integrability and Quantization I
Varna, Bulgaria: September 1–10, 1999. - Summer School on Differential Geometry
Coimbra, Portugal: September 3–7, 1999 - International Congress of Mathematicians (ICM 1998)
Berlin, Germany: August 18–27, 1998 - Second Meeting on Quaternionic Structures in Mathematics and Physics
Roma, Italy: September 6–10, 1999 - Meeting on Quaternionic Structures in Mathematics and Physics
Trieste, Italy: September 5–9, 1994 - The International Conference on Secondary Calculus and Cohomological Physics
Moscow, Russia: August 24–August 31, 1997 - 1st International Meeting on Geometry and Topology
Braga, Portugal: September 11–13, 1997 - 9th International Conference on Domain Decomposition Methods
Ullensvang, Norway: June 3–8, 1996 - XIV C.E.D.Y.A. / IV C.M.A.
Vic, Spain: September 18–22, 1995 - Nonlinear Analysis, Function Spaces and Applications Vol. 6
Prague, Czech Republic: May 31–June 5, 1998 - Nonlinear Analysis, Function Spaces and Applications Vol. 5
Prague, Czech Republic: May 23–28, 1994 - Function Spaces, Differential Operators and Nonlinear Analysis
Paseky na Jizerou, Czech Republic: September 3–9, 1995 - Surgery and Geometric Topology
Josai University, Sakado, Japan: September 17–20, 1996 - 3rd International Conference on Approximation and Optimization in the Caribbean
Puebla, Mexico: October 8–13, 1995 - 7th International Conference on Differential Geometry and Its Applications
Brno, Czech Republic: August 10–14, 1998 - 6th International Conference on Differential Geometry and Its Applications
Brno, Czech Republic: August 28–September 1, 1995 - 5th International Conference on Differential Geometry and Its Applications
Opava, Czechoslovakia: August 24–28, 1992
Nov 16, 2013
Differential Geometry: A beginner's journey.
A good summary:
http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf
Focusing on surface:
http://en.wikipedia.org/wiki/Differential_geometry_of_surfaces?action=render
Applications of Differential Geometries:
Helping to solve other unsolved maths problem:
http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics
http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics
Possible applications of differential geometry concepts:
Elementary Geometry
- Center of an arc determined with straightedge and compass.
- Surface areas: Circle, trapezoid, triangle, sphere, frustum, cylinder, cone...
- Power of a point with respect to a circle.
- Euler's line goes through the orthocenter, the centroid and the circumcenter.
- Euler's circle is tangent to the incircle and the excircles (Feuerbach, 1822).
- Barycentric coordinates & trilinears examplify homogeneous coordinates.
- Elliptic arc: Length of the arc of an ellipse between two points.
- Perimeter of an ellipse. Exact formulas and simple ones.
- Circumference of an ellipse: Unabridged discussion.
- Surface of an ellipse.
- Volume of an ellipsoid (either a spheroid or a scalene ellipsoid).
- Surface area of a spheroid (oblate or prolate ellipsoid of revolution).
- Quadratic equations in the plane describe ellipses, parabolas, or hyperbolas.
- Centroid of a circular segment. Find it with Guldin's (Pappus) theorem.
- Parabolic arc of given extremities with a prescribed apex between them.
- Focal point of a parabola. y = x 2 / 4f (where f is the focal distance).
- Parabolic telescope: The path from infinity to focus is constant.
- Make a cube go through a hole in a smaller cube.
- Octagon: The relation between side and diameter.
- Constructible regular polygons and constructible angles (Gauss).
- Areas of regular polygons of unit side: General formula & special cases.
- For a regular polygon of given perimeter, the more sides the larger the area.
- Curves of constant width: Reuleaux Triangle and generalizations.
- Irregular curves of constant width. With or without any circular arcs.
- Solids of constant width. The three-dimensional case.
- Constant width in higher dimensions.
- Fourth dimension. Difficult to visualize, but easy to consider.
- Volume of a hypersphere and hyper-surface area, in any dimensionality.
- Hexahedra. The cube is not the only polyhedron with 6 faces.
- Descartes-Euler Formula: F-E+V=2 but restrictions apply.
Topology:
- Metric spaces: The motivation behind more general topological spaces.
- Abstract topological spaces are defined by calling some subsets open.
- Closed sets are sets (of a topological space) whose complements are open.
- Subspace F of E: Its open sets are the intersections with F of open sets of E.
- Separation axioms: Flavors of topological spaces, according to Trennung.
- Compactness of a topological space: Any open cover has a finite subcover.
- Real-valued continuous functions on compact sets attain their extremes.
- Borel sets. Tribes form the topological foundation for measure theory.
- Locally compact sets contain a compact neighborhood of every point.
- General properties of sequences characterize topological properties.
- Continuous functions let the inverse image of any open set be open.
- Restrictions remain continuous. Continuous extensions may be impossible.
- The product topology makes projections continuous on a cartesian product.
- Tychonoff's Theorem: Any product of compact spaces is compact.
- Connected sets can't be split by open sets. The empty set is connected.
- Path-connected sets are a special case of connected sets.
- Homeomorphic sets. An homeomorphism is a bicontinuous function.
- Arc-connected spaces are path-connected. The converse need not be true.
- Homotopy: A progessive transformation of a function into another.
- The fundamental group: The homotopy classes of all loops through a point.
- Homology and Cohomology. Poincaré duality.
- Descartes-Euler Formula: F-E+V = 2, but restrictions apply.
- Euler Characteristic: c (chi) extended beyond its traditional definition...
- Winding number of a continuous planar curve about an outside point.
- The dog on a leash theorem.
- A topological proof of the fundamental theorem of algebra.
- Fixed-point theorems by Brouwer, Shauder and Tychonoff.
- Turning number of a planar curve with a well-defined oriented tangent.
- Real projective plane and Boy's surface.
- Hadwiger's additive continuous functions of d-dimensional rigid bodies.
- Eversion of the sphere. An homotopy can turn a sphere inside out.
- Classification of surfaces: "Zero Irrelevancy Proof" (ZIP) by J.H. Conway.
- Braid groups: Strands, braids and pure braids.
Completeness:
- Complete metric space: A space in which all Cauchy sequences converge.
- Flawed alternatives to completeness.
- Banach spaces are complete normed vector spaces.
- Fréchet spaces are generalized Banach spaces.
Fractal Geometry:
- Fractional exponents were first conceived by Nicole d'Oresme (c. 1360).
- The von Koch curve (and snowflake): Dimension of self-similar objects.
- Hausdorff dimension is revealed by a covering with balls of radius < e.
- The Julia set and the Fatou set of an analytic function are complementary.
- The Mandelbrot set was so named by Adrien Douady & John H. Hubbard.
Angles and Solid Angles:
- Planar angles (from one direction to another) are signed quantities.
- Bearing: Unless otherwise specified, this is the angle west of north.
- Solid angles are to spherical patches what planar angles are to circular arcs.
- Circular measures: Angles and solid angles aren't quite dimensionless...
- Solid angle formed by a trihedron : Van Oosterom & Strackee (1983).
- Solid angle subtended by a rhombus. Apex of a right rhombic pyramid.
- Formulas for solid angles subtended by patches with simple shapes.
- Right ascension and declination. Precession of celestial coordinates (a,d).
Curvature and Torsion:
- Curvature of a planar curve: Variation of inclination with distance dj/ds.
- Curvature and torsion of a three-dimensional curve.
- Distinct curvatures and geodesic torsion of a curve drawn on a surface.
- The two fundamental quadratic forms at a point of a parametrized surface.
- Lines of curvature: Their normal curvature is extremal at every point.
- Geodesic lines. Least length is achieved with zero geodesic curvature.
- Meusnier's theorem: Tangent lines have the same normal curvature.
- Gaussian curvature of a surface. The Gauss-Bonnet theorem.
- Parallel-transport of a vector around a loop. Holonomic angle of a loop.
- Total curvature of a curve. The Fary-Milnor theorem for knotted curves.
- Linearly independent components of the Riemann curvature tensor.
Planar Curves:
- Cartesian equation of a straight line: passing through two given points.
- Confocal Conics: Ellipses and hyperbolae sharing the same pair of foci.
- Spiral of Archimedes: Paper on a roll, or groove on a vinyl record.
- Hyperbolic spiral: The inverse of the Archimedean spiral.
- Catenary: The shape of a thin chain under its own weight.
- Witch of Agnesi. How the versiera (Agnesi's cubic) got a weird name.
- Folium of Descartes.
- Lemniscate of Bernoulli: A quartic curve shaped like the infinity symbol.
- Along a Cassini oval, the product of the distances to the two foci is constant.
- Limaçons of Pascal: The cardioid (unit epicycloid) is a special case.
- On a Cartesian oval, the weighted average distance to two poles is constant.
- The envelope of a family of curves is everywhere tangent to one of them.
- The evolute of a curve is the locus of its centers of curvature.
- Involute of a curve: Trajectory of a point of a line rolling on that curve.
- Parallel curves share their normals, along which their distance is constant.
- The nephroid (or two-cusped epicycloid ) is a catacaustic of a circle.
- Freeth's nephroid: A special strophoid of a circle.
- Bézier curves are algebraic splines. The cubic type is the most popular.
- Piecewise circular curves: The traditional way to specify curved forms.
- Intrinsic equation [curvature as a function of arc length] may have spikes.
- The quadratrix (trisectrix) of Hippias squares the circle and trisects angles.
- The parabola is constructible with straightedge and compass.
- Mohr-Mascheroni constructions use the compass alone (no straightedge).
http://demonstrations.wolfram.com/siteindex.html
Nov 13, 2013
Nov 9, 2013
A generalization of a number pattern from base 10 to base 16, and base 20, and base 32
First looking at the decimals number patterns:
12*9+3 : 111
123*9+4 : 1111
1234*9+5 : 11111
12345*9+6 : 111111
123456*9+7 : 1111111
1234567*9+8 : 11111111
12345678*9+9 : 111111111
123456789*9+10 : 1111111111
And the python generator for this:
def get_first(p1, mynum):
p2 = p1 + str(mynum)
n2 = int(p2) * 9 + (mynum+1)
print "%s*9+%d : %d"%(p2,mynum+1, n2)
get_first(p2, mynum+1)
get_first("1", 2)
Can it be generalize to base 16?
Yes:
12*15+0x3 : 0x111
123*15+0x4 : 0x1111
1234*15+0x5 : 0x11111
12345*15+0x6 : 0x111111
123456*15+0x7 : 0x1111111
1234567*15+0x8 : 0x11111111
12345678*15+0x9 : 0x111111111L
123456789*15+0xa : 0x1111111111L
123456789a*15+0xb : 0x11111111111L
123456789ab*15+0xc : 0x111111111111L
123456789abc*15+0xd : 0x1111111111111L
123456789abcd*15+0xe : 0x11111111111111L
123456789abcde*15+0xf : 0x111111111111111L
123456789abcdef*15+0x10 : 0x1111111111111111L
And the program is:
def pattern_base16(p1, mynum):
p2 = p1 + hex(int(str(mynum)))[2:]
n2 = int(p2,16) * 15 + (mynum+1)
print "%s*15+%s : %s"%(p2,hex(mynum+1), hex(n2))
pattern_base16(p2, mynum+1)
pattern_base16("1", 2)
And for base 20:
12*19+3 : 111
123*19+4 : 1111
1234*19+5 : 11111
12345*19+6 : 111111
123456*19+7 : 1111111
1234567*19+8 : 11111111
12345678*19+9 : 111111111
123456789*19+a : 1111111111
123456789a*19+b : 11111111111
123456789ab*19+c : 111111111111
123456789abc*19+d : 1111111111111
123456789abcd*19+e : 11111111111111
123456789abcde*19+f : 111111111111111
123456789abcdef*19+g : 1111111111111111
123456789abcdefg*19+h : 11111111111111111
123456789abcdefgh*19+i : 111111111111111111
123456789abcdefghi*19+j : 1111111111111111111
123456789abcdefghij*19+10 : 11111111111111111111
and the program is:
from baseconv import BaseConverter
def base10_to_20(nos):
base20 = BaseConverter('0123456789abcdefghij')
return base20.encode(nos)
def base20_to_10(mystring):
base20 = BaseConverter('0123456789abcdefghij')
return int(base20.decode(mystring))
def pattern_base20(p1, mynum):
p2 = p1 + base10_to_20(mynum)
#print "p2=%s"%p2
n2 = base20_to_10(p2) * 19 + (mynum+1)
print "%s*19+%s : %s"%(p2, base10_to_20(mynum+1), base10_to_20(n2))
pattern_base20(p2, mynum+1)
pattern_base20("1", 2)
And for base 32:
12*31+3 : 111
123*31+4 : 1111
1234*31+5 : 11111
12345*31+6 : 111111
123456*31+7 : 1111111
1234567*31+8 : 11111111
12345678*31+9 : 111111111
123456789*31+a : 1111111111
123456789a*31+b : 11111111111
123456789ab*31+c : 111111111111
123456789abc*31+d : 1111111111111
123456789abcd*31+e : 11111111111111
123456789abcde*31+f : 111111111111111
123456789abcdef*31+g : 1111111111111111
123456789abcdefg*31+h : 11111111111111111
123456789abcdefgh*31+i : 111111111111111111
123456789abcdefghi*31+j : 1111111111111111111
123456789abcdefghij*31+k : 11111111111111111111
123456789abcdefghijk*31+l : 111111111111111111111
123456789abcdefghijkl*31+m : 1111111111111111111111
123456789abcdefghijklm*31+n : 11111111111111111111111
123456789abcdefghijklmn*31+p : 111111111111111111111111
123456789abcdefghijklmnp*31+q : 1111111111111111111111111
123456789abcdefghijklmnpq*31+r : 11111111111111111111111111
123456789abcdefghijklmnpqr*31+s : 111111111111111111111111111
123456789abcdefghijklmnpqrs*31+t : 1111111111111111111111111111
123456789abcdefghijklmnpqrst*31+u : 11111111111111111111111111111
123456789abcdefghijklmnpqrstu*31+v : 111111111111111111111111111111
123456789abcdefghijklmnpqrstuv*31+w : 1111111111111111111111111111111
123456789abcdefghijklmnpqrstuvw*31+10 : 11111111111111111111111111111111
And the program is:
from baseconv import BaseConverter
def base10_to_32(nos):
base32 = BaseConverter('0123456789abcdefghijklmnpqrstuvw')
return base32.encode(nos)
def base32_to_10(mystring):
base32 = BaseConverter('0123456789abcdefghijklmnpqrstuvw')
return int(base32.decode(mystring))
def pattern_base32(p1, mynum):
p2 = p1 + base10_to_32(mynum)
#print "p2=%s"%p2
n2 = base32_to_10(p2) * 31 + (mynum+1)
print "%s*31+%s : %s"%(p2, base10_to_32(mynum+1), base10_to_32(n2))
pattern_base32(p2, mynum+1)
The BaseConverter python module is downloaded following the two articles below:
http://stackoverflow.com/questions/2267362/convert-integer-to-a-string-in-a-given-numeric-base-in-python
https://bitbucket.org/semente/baseconv
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