tag:blogger.com,1999:blog-62081078043561184322014-10-06T20:11:42.722-07:00About MathematicsBill Harfordhttp://www.blogger.com/profile/06941521455903170510noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6208107804356118432.post-18141512347364689822011-11-20T11:51:00.000-08:002011-11-20T11:51:02.230-08:00What Has to be Done When Someone Uses the Word "Logic"<div dir="ltr" style="text-align: left;" trbidi="on">When someone uses the word "logic"he/she should immediately point out what is initially assumed to be true/false and what truth results is derived, i.e. what can be proved from those initial assumptions.Word logic is nice to use, it can be fancy, it can show you want to be precise in your communication or explanation. However, the axiomatic system should be known and understandable for all the parties that are part of the "logic" communication. Saying that something is logical doesn't mean it is obvious, and it doesn't mean it does not require a proof. If something appear to be "trivial", the logical context of axioms and premises should be clear to all participants who want to accept that "trivial" remark. Contextually "trivial" is OK.<br /><br /><br /><br /><br />[ logic, mathematical logic, math, math concepts, axioms, ]</div>Bill Harfordhttp://www.blogger.com/profile/06941521455903170510noreply@blogger.com0tag:blogger.com,1999:blog-6208107804356118432.post-13714415840859215392011-07-01T08:29:00.000-07:002011-07-01T09:39:06.595-07:00Learning and Understanding Mathematics - Please Visit My Brand New Blog at About Mathematics and Real World Mathematics ApplicationsLearning and Understanding Mathematics - Please Visit My Brand New Blog at<br /><a href="http://explainingmath.blogspot.com/">About Mathematics and Real World Mathematics Applications</a><br /><br />There you can find posts about mathematics and real life mathematics applications:<br /><br />Real world examples for rational numbers, for kids<br />Math and its relationship with real world<br />How math can be applied to so many different fields?<br />Where the graphs in mathematics and physics come from?<br />Tweets about math, physics, and how to approach math calculations<br />One insight about mathematical axioms, logic and their relation to other disciplines<br />How the ideas are born and notes on creative thinking<br />Mathematics Axiomatic Frontier<br />Why math can be an independent discipline?<br />More on creative thinking, math, innovations, physics, emotions<br />Comparison between making movies and math and physics<br />More tweets about math<br />Domains of math applications and math development<br />Where all those number series in math are coming from?<br />How to understand the role of math in economics, physics, engineering, and in other fields<br /><br /><br />More articles to come. Topics will include "From Sets to Numbers to Mathematical Functions" and "What Does That 'Let's assume we have...' Mean in Mathematics?", and more.<br /><br />In combination with vivid real world examples, I will try to show you how to think mathematically, when to think mathematically, and what are the general rules for you to solve mathematical problems and to define new ones, your own, from scratch. My goal is to show you the methods to use with mathematics and to reveal the motivation behind mathematical directions of development.<br /><br />You can find elsewhere how to solve equations and work with algebra, how to do the integration, calculate matrices. But, at one point you may ask yourself, where all that mathematics comes from? Why there are algebra and quadratic equations, and so many other equations, at the first place? What would be the way to understand them better? How you can apply concepts in math in real world, the one you see immediately when you close the mathematics textbook and look around?<br /><br />I will demonstrate you the methods, the way of approach, the directions of thinking that will help answering all these questions.<br /><br />How math can be a part of physics, economics, engineering, chemistry, finance, commerce, trading, accounting, and yet, mathematics can exists as a separate and independent discipline, from all of the fields it is applied to? What is the point at which mathematics took off as a separate discipline? I am answering these questions in my blog.Bill Harfordhttp://www.blogger.com/profile/06941521455903170510noreply@blogger.com0