Plus I thought it might be a fun post and unlike the Wired list this one goes to eleven. So here they are in no particular order:
Plus I thought it might be a fun Key formulas equations 2 and unlike the Wired list this one goes to eleven. So here they are in no particular order: It is central to Combinitorics which has connections to many areas of math, I guess I should qualify that if you are serious about computer science and math related programming topics then you should be able to recite and apply it from memory, even when you are drunk, sleep deprived or being held at gun point.
Ok that might be a bit much but you get the idea. Also these two formulas are categorical duals of each other, which means that if one were smart and had a good grasp of Category Theory we could probably be really OCD about it and get it down to one formula. Understanding Set Theory and Boolean Algebra are very important basic concepts in our profession and the Boolean version can make you better programmer, as you can use it to refactor logical if statements.
Eigenvector and Eigenvalue This equation and these concepts are not only central to Linear Algebra but these Linear Algebraic ideas and others are both used and extend into many other areas of math including Linear Transformations and Graphs in terms of matrices like the Adjacency Matrix and much more.
Linear Algebra is becoming increasingly central to the types of things we are doing in our profession, it is used heavily in Statistics and Machine Learning not to mention the Page Rank Algorithm is based in part on this equation. The problem is that these two are pretty different from other areas of math in terms of "Equations" I tried to think of some basic Ideas and The Pumping Lemma came to mind, and I found the above formula concisely expressed on Wikipedia.
This version of the Pumping Lemma is a more limited version of Another Theory which is used to check whether a Language is Regular. Also this is maybe not the best choice as it is pretty dense, if you want a better explanation I recommend this.
While this "equation" is pretty specialized, it is actually a special case of the more general Iteration Theorem, the real point here is really about more general domain knowledge. It is central to what you do every day you are programming such as compilers and regular expressions not to mention the almost ubiquitous Kleene Star.
Interestingly this area has a parallel in the physical word, in terms of Thermodynamic Entropywhich also parallels the Boltzman Equation mentioned in the Wired Article. In programming and computer science information is our business and these ideas are central to many things that we deal with especially the storage, transmission, computational transformation like compressionand computation of information.
It rose from obscurity to being used for spam detection and with such applications as classifiersMachine LearningData Mining and more. Mathematically it is part of a rift in statistics and probability and I confess I may not yet call myself " an initiate of the bayesian conspiracy " but it hard to deny its utility plus there seems to be a more axiomatic basis that relates to Boolean Logic Set Theory, which makes it all the more alluring.
Natural Join is the Cartesian Product of two tables selecting matching rows and eliminating duplicate columns. The Relational Algebra is in my opinion a bit of an odd beast when it comes to algebraic structures, but if you use SQL you are already using an implementation of it.
As data persistence becomes more heterogeneous I think understanding these concepts, will become more important. The Fixed-Point Y Combinator Just as we need a "equation" from Formal Language Theory or Automata Theory we really should have one that is related to Lambda Calculusin this case this equation is in the untyped lambda calculus.
Even though the Fixed-point Combinator stands up on its own, it is fairly well known, well at least in name due to the use of it by Paul Graham for his incubator Y-Combinator. The Fixed-Point Combinator allows one to implement anonymous recursion which is a powerful programming technique. It also ties into some deeper theoretical aspects of computer science and logic such as Combinatory Logic.
Also the following is a definition of lim sup Limit Superior: Where inf is infimum and sup is supremum two concepts that seem to show up quite a bit especially when you are concerned with bounds like with Lattices and they also seem to show up in relation to Topology.
And we all know why we should care about his one: These formulas will give one a better understanding complex numbers which are needed in other areas of advanced math also these formulas relate to Fourier Analysis which does have applications in Computer Science.
I am curious to see how well this list holds up, how will I feel about it in a year? Also in writing this I realized that I still have quite a bit more to learn about at least half of this list, if not all of it, which made it hard to write as it was quite a little unfinished research project.
I hope you enjoyed it as much as I did writing it. The Set Universe is the upper bound and the empty set is the lower bound.Physics Equations and Formulas By Steven Holzner Part of the Physics I For Dummies Cheat Sheet Physics is filled with equations and formulas that deal with angular motion, Carnot engines, fluids, forces, moments of inertia, linear motion, simple harmonic motion, thermodynamics, and work and energy.
Question 4: Students will see that, as with linear equations, literal equations can be solved in different ways.
Students can show that both solutions are the same by finding a common denominator for the two fractions under method 1. Free Algebra 2 worksheets created with Infinite Algebra 2. Printable in convenient PDF format. rutadeltambor.comA.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
For example, represent inequalities describing nutritional and cost constraints on . Tips to Remember When Graphing Systems of Equations. Graph each equation on the same graph. If the equation is written in standard form, you can either find the x and y intercepts or rewrite the equation in slope intercept form.
Mathematical Formulas Coffee Mug - Ponder Famous Math Equations While You Enjoy Your Drink - Comes in a Fun Gift Box - by The Unemployed Philosophers Guild.