Appetizers and Lessons for Mathematics and Reason - Entrance Level 
||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

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YOU are better than YOU think. Show yourself  how:

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Read  logic chapters 1 to 5  in online volume Three Skills for Algebra  
Then seek 4 skills for algebra in it.

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 Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and
writing

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.


After logic  (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;

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Caution: Site advice is approximately correct, for some circumstances, not all. That leaves room for thought

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What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts.


Try the Twiddla Whiteboard. In principle, it  allows to people to draw and chat together online on a copy of this webpage or a clean sheet. The chat may be via text or audio.  Visit www.twiddla.com to set up whiteboards to work with the webpage of your choice.

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

 

Books by other authors 

  • Mathematics from the Birth of Numbers, 1996, 950+, by the late Jan Gullberg, is an excellence resource forpupils and instructor in college and the upper years of secondary schools. ISBN 0-393-04002-X.  The book is a work of love by its author, one that I would highly recommend as gift for any one with a strong interest in learning or teaching mathematics. 

  • The VNR Concise Encyclopedia of Mathematics by W. Gellert, H. Küstner, M. Hellwich & H. Kästner, Van Nostrand Reinhold Company, 1975 (or 1977). ISBN: 0-442-22646-2 (hard cover) and ISBN:0-442-22647-0 (paperback). Copy right held by a corporation whose sense of public service does not exist or is insufficient to put this work back in print.  Used copies available.
  • Collin's Dictionary of Mathematics - Undergraduates and high school instructors may find it useful.. ISBN 0-00-710295-X  My copy was found in the McGill U. Bookstore for 24 $CDN.  www.collins.co.uk

More recommendations for public and private libraries with links to Amazon

Review

Calculus with Analytic Geometry, Denis Zill, Here is another well-written calculus book. A colleague of mine like it so much that he provided feedback to the author to help remove typos. Copies should be in every college library. Here is a good reference for a first course or two in calculus. 
Calculus of One and Several Variables. Einar Hille and Satunino L. Salas. Here is or was a good reference for calculus - an easier read than most. Copies should be in every college library.
Mathematics from the Birth of Numbers, Jan Gullerg. This is a work of love by the author with help from his family.  This hardcopy has over a 1004 pages, all beautifully typeset.  The word beautiful when applied to this work is an understatement. I recommend it to all high school and college instructors and tutors, and college level students in math, science or engineering. High school and college libraries should, no must, add this work to their collections.
Every high school and college library should have a hardcopy of this work. If only used copies are available, get a used one and rebind it. This work is a must. 
Mathematics for the Non-Mathematician. Morris Kline is one of my favorite authors. A recent acquisition. Prerequisite: A first or further course in calculus. My review to come. I am still reading it. 
Mathematical Thought from Ancient to Modern Times, Volumes I to III,  by Morris Kline.  All college and university libraries should have this work and its companion.  

Prerequisite: An undergraduate degree in Mathematics with a strong interest in the logic of mathematics.

Mathematics, the Loss of Certainty. Morris, Kline; Hardcover. Mathematics may be the queen of science and logic, but the certainty we once held or aspired to in this subject is not absolute.

Prerequisite: An undergraduate degree in Mathematics with a strong interest in the logic of mathematics.

Calculus, Lipman Bers, Here is a rare and beautiful calculus book which dared in the 1960s mention decimals in the representation of real numbers. Elements of this work should return to the calculus curriculum. Copies should be in every college library.
Principles of Real Analysis, Walter Rudin.   Here is a good reference for advanced students in mathematics, physics and electrical engineering.   

Prerequisite: Two or three courses in calculus. 

Introduction to Topology. Bert Mendolson. As a undergraduate, I found the introduction to topology in real analysis too hard for my liking.  This work (if I remember correctly) clarified matters - made them simpler. 

Co-requisite: A first course in real analysis. 

Advanced Calculus, Loomis and Sternberg. Here is a Banach space approach to advance calculus.  See treatment of chain-rule via linear approximation and a careful use of little o and big O asymptotic behaviors.  Out of Print.  Used copies may be available.  This work includes the proofs normally omitted in first courses in calculus. 

Co-requisite: A first course in real analysis. 

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