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Finite and Infinite Mathematics:
Sets, Numbers, Lines, Equations, Probability

ISBN 978-1-4636-9269-8



Rational Thinking, Government Policies, Science, and Living
ISBN 978-1-4538-1835-0


Teaching and Helping Students
ISBN 978-1-4196-7435-8

Teaching and learning mathematics and physics
Analyze all the facts, and find knowledge of that which you wish to know.
Dr. Sanford Aranoff

Currently Adjunct Associate Professor of Science and Mathematics at Rider University
High school educator, including mentoring new mathematics teachers

List of publications: Here are of my most recent papers.

Basic Assumptions and Black Holes , Physics Essays 26, 110 (2013).
Reprinted by permission of Physics Essays Publication, from Physics Essays.

Comment on “New insights into Gödel’s universe without time” , Physics Essays 26, 577 (2013).
Reprinted by permission of Physics Essays Publication, from Physics Essays.

Postulates of Special Relativity, Physics Essays 22, 559 (2009).
Reprinted by permission of Physics Essays Publication, from Physics Essays.

The Enlightenment and Western Civilization, PHILICA.COM, article number 402 (2014).

The Aura of Einstein and General Relativity, PHILICA.COM, article number 192 (2010).

Time Does Not Exist, and the Incompleteness of Knowledge , PHILICA.COM, article number 188 (2010).
Current physical theory is that time does not exist. This paper gives simple clarifications of this idea. It incudes a discussion of God. What is time? See Comment on “New insights into Gödel’s universe without time” , Physics Essays 26, 577 (2013).

Abortion and the Beginning of a Person , PHILICA.COM , article number 189 (2010).
The views of various writers on abortion are discussed. Kenny quotes the Bible saying abortion is murder. Kenny's errors in readings from the Bible, and his ignoring self-defense, are discussed, along with the use of the Bible to discuss American law and our morals. Warren uses philosophical arguments to say a fetus is not a person. These diverse viewpoints are reconciled by saying abortion is immoral but not murder. Moral questions regarding abortion are discussed. A novel philosophical idea, the reality of organization, is introduced to differentiate between a fetus and a baby. Defining personhood based on organization has implications for the future as computers become more powerful than people.

To Teach, We Need To Build the Course Around Principles
Published in Gifted Education Press Quarterly,Spring 2014.

Professors Substituting In High School
Published in Gifted Education Press Quarterly,Winter 2013.

Lessons We Can Learn from Bill Gates’ Dropping Out of Harvard University
Published in Gifted Education Press Quarterly, Fall 2011.

To Educate the Gifted, We Need To Stress Basic Principles
Published in Gifted Education Press Quarterly, Winter 2009.

How is a Teacher of the Gifted Supposed to Teach?
Published in Gifted Education Press Quarterly, Fall 2009.

What Young Teachers of the Gifted Need to Know and Do
Published in Gifted Education Press Quarterly, Winter 2008.

"The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics," Review on of the book on amazon.com. Click on customer reviews.

Some more papers in peer-reviewed physics journals:

Equilibrium in Special Relativity

Few-Phonon Structure Functions for Liquid Helium II

Teaching and Helping Students

These are things I said teaching to help clarify the ideas to the students. This will help students to think better and clearer, to enjoy school and to be happy, to do better on tests and to get better grades, and to be more successful in life. Teachers and profesors can read this to get ideas how to better teach and to relate to the students. There is nothing as exciting as working with young minds!

This file which you can read now contains selections from the book. It is organized like a Help file, with table of contents, topics and subtopics, index, and search.

Some things in the book:

Why do elephants have big ears?
Why do we not fall when leaning on a moving bicycle?
Arithmetic and geometric mean
Boredom in school. If you feel good, you understand it correctly.

Here is what some teachers wrote:

This is an excellent resource for math teachers, both secondary and otherwise. I am a first year teacher and have been searching for resources like this - I saved it to disk and will definitely refer to it again!

I found your classroom tips to be valuable and will put them into practice in my classroom!

Excellent ideas and techniques!

Thank you! This has much more than how to teach math and science. It's a great resource!

Cosmic rays create clouds. Sunspot activity is responsible for climate change, not human activity.

Other publications on various subjects:

Biblical Prophecies. The Hebrew Bible clearly predicts the reestablishment of modern Israel and its continuing survival.

Suggestions and thoughts:

Here are some suggestions and thoughts that have helped me over the years, which I am happy to share with you:

Give people attention. Focus on each person. Keeping people happy is an excellent objective.

Presentations: Conclusion, significance, supporting details. The wrong way is topic, sentence, body, conclusion.

Here are ideas about thinking. Don't rush - think.

What's the problem?

1. Ask yourself, "What's the problem (or difficulty)?" Check that it is correctly stated.
2. Start from the beginning.
3. It you do not know how to start, pause, relax, and study it. Jot down possible ideas. Put your full attention on each detail of the theory and problem.
4. Check everything.
5. Smile.

How to check:

1. See if it is worked out orderly. Be sure that the work is neat.
2. Routine check down the line to see if everything is correct.
3. Study, think, and analyze concepts if they are correct. Be sure that you know what everything means, and why. 4. Check arithmetic, signs, units, formulas, numerical quantities, algebra, each item separately.
5. Check if anything omitted. Check that everything is checked properly.
6. Review it after a pause of a moment, hour, or a couple of days. Check everything. Apply it. Discuss it with someone else.

Comments:

The idea is to start from the beginning and to check every single thing several ways.
True for thinking, checking, memorizing, and explaining.

Smile!

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