Author Archives: vinaire

I am originally from India. I am settled in United States since 1969. I love mathematics, philosophy and clarity in thinking.

Algebra Review

pre-algebra

Reference: Remedial Math

For application by the student

UNIT 1: Real Numbers

Answers to Unit 1

UNIT 2: Variable Expressions

Answers to Unit 2

UNIT 3: Solving Equations

Answers to Unit 3

UNIT 4: Applications

Answers to Unit 4

UNIT 5: Polynomials

Answers to Unit 5

UNIT 6: Factoring

Answers to Unit 6

UNIT 7: Algebraic Functions

Answers to Unit 7

UNIT 8: Graphs & Linear Equations

Answers to Unit 8

UNIT 9: Systems of Linear Equations

Answers to Unit 9

UNIT 10: Inequalities

Answers to Unit 10

UNIT 11: Radical Expressions

Answers to Unit 11

UNIT 12: Quadratic Equations

Answers to Unit 12

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Remedial Math Level 2B

mc-001

Middle School Review 2B

Lesson 7: Equations & Transposition

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Primary School Review

numbers2

Reference: Remedial Math

Lesson 1: Numbers

Exercise: Reading Numbers from Dubb 

Exercise: Writing Numbers from Dubb 

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Lesson 2: Addition

Exercise: Addition Problems from Dubb

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Lesson 3: Multiplication

Exercise: Multiplication Problems from Dubb

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Lesson 4: Subtraction

Exercise: Subtraction Problems from Dubb

Exercise: Integer Problems from Dubb

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Lesson 5: Division

Exercise: Short Division Problems from Dubb

Exercise: Long Division Problems from Dubb

Exercise: Arithmetic Expression Problems from Dubbs

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Lesson 6: Units

Table for the Units of Measure

Exercise: Problems on Units from Dubb

Long Measure

Square Measure

Rectangles

Cubic Measure

Time Measure

Miscellaneous Tables

Promiscous Examples

Addition of Compound Numbers

Subtraction of Compound Numbers

Time between two Dates

Time in Days between Two Dates

Multiplication of Compound Numbers

Division of Compound Numbers

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Program 1: A Level 1 Math Program

To be used for a summary review of Level 1.

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DETAILED VERSIONS

To be used for children needing more details.

MS A1 Numbers

MS A2 Addition

MS A3 Subtraction

MS A4 Multiplication

MS A5 Division

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The Mindfulness Guide

Mindfulness Guide

Reference: Mindfulness Approach

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The role of the mindfulness guide is to help reestablish the ability of a person to think for himself. This is done by resolving all unassimilated nodes in the person’s mental matrix. The mindfulness guide does not assert any control over the other person.

The mindfulness guide acts as follows when guiding another person.

ACT ONE: He must review his commitment to restore the other person’s ability to think for himself.

ACT TWO: He must establish himself simply as a guide in the mind of the other person, and not as some authority.

ACT THREE: His beginning actions are to clean up the anomalies currently absorbing the other person’s attention. He does that by listening to the other person and acknowledging his concerns. He then explains the discipline of mindfulness, and how it can handle the other person’s concerns.

ACT FOUR: His next action is to establish in the other person the understanding of the discipline of mindfulness through the exercises Mindfulness meditation and Discerning the Environment. He then helps the person unwind his mind through the exercise, Accessibility of Memory.

This approach shall help extrovert the person’s attention and help him think more clearly. This is especially vital for heavily introverted cases.

The mindfulness guide then helps the other person become a mindfulness practitioner by practicing subsequent exercises as laid out here.

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Universe, the Beginning

Reference: The Creation Hymn of Rig Veda

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Here we have the Ancient Creation Hymn along with a modern scientific rendition.

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There was neither non-existence nor existence then.
There was neither the realm of space nor the sky which is beyond.
What stirred?
Where?
In whose protection?
Was there water, bottomlessly deep?

Prior to the universe there was no idea of existence or non-existence.

There was no awareness of matter, energy, space or time.

The universe seems to arise from some disturbance 

Of what? We do not know.

There was neither death nor immortality then.
There was no distinguishing sign of night nor of day.
That One breathed, windless, by its own impulse.
Other than that there was nothing beyond.

There was no idea of death or immortality then.

There was neither day nor night.

There was only the slightest awareness

Of motion appearing by itself

Darkness was hidden by darkness in the beginning,
with no distinguishing sign, all this was water.
The life force that was covered with emptiness,
that One arose through the power of heat.

Lack of motion was hidden by lack of awareness

Nothing was distinguishable, everything was the same

The motion that arose was surrounded by no motion

There alone was the power of awareness.

Desire came upon that One in the beginning,
that was the first seed of mind.
Poets seeking in their heart with wisdom
found the bond of existence and non-existence.

It was the desire that was the disturbance

It was the beginning of the mind

There was then the awareness of existence

That also brought the awareness of non-existence.

Their cord was extended across.
Was there below?
Was there above?
There were seed-placers, there were powers.
There was impulse beneath, there was giving forth above.

Scale was formed from physical motion to metaphysical awareness, 

All opposites, such as below and above, had a scale as well.

There was concrete reality, and the abstraction underlying it

There was desire below,  and there was change above.

Who really knows?
Who will here proclaim it?
Whence was it produced?
Whence is this creation?
The gods came afterwards, with the creation of this universe.
Who then knows whence it has arisen?

Before the beginning of awareness

There was non-awareness

Before the beginning of motion

Who would know what was there?

Any knower came afterwards with the creation

Who then knows how disturbance came to be?

Whence this creation has arisen
– perhaps it formed itself, or perhaps it did not –
the One who looks down on it,
in the highest heaven, only He knows
or perhaps He does not know.

The beginning of the universe is there

Perhaps it formed itself, or perhaps it did not

Maybe the broadest viewpoint of it

Could reveal the secret of the beginning

Or, perhaps, it may not.

 

Summary

  1. We do not know what was there prior to the beginning of the universe. So, we shall call that state BRAHMAN as referred to in the ancient Vedas. This is also the “noumenon” of Kant.

  2. The universe seems to arise from the disturbance of this earlier state of BRAHMAN, or absolute zero. This beginning is characterized by motion and awareness. This is also the “phenomenon” of Kant.

  3. When there is motion there is also awareness. When there is no motion there is no awareness. Thus, motion and awareness present two different aspects of disturbance.

  4. The dimension of disturbance may be represented by a ‘concrete-to-abstract’ scale with concrete motion at one end also appearing as abstract awareness at the other end.

  5. This scale may be formalized as physical motion that is getting increasingly abstracted as metaphysical awareness.

  6. Thus there is a gradient of abstraction from PHYSICAL to METAPHYSICAL just like there is a gradient of temperature from HOT to COLD.