Testing

Hey guys, Im testing out ways of putting equations directly into the blog

Let me know what you think

Top of the rollercoaster

500 C.E.


Metrodorus (c. 500)
Anicius Maulius Severinus Boethius (c. 480-524)
Simplicius of Cilicia (c. 530)
Anthemius of Tralles (d. c. 534)
Aryabhata (476-c. 550)
Flavius Magnus Aurelius Cassiodorus (c. 480-c. 575)
John Philoponus (c. 490)
Varahamihira (c. 505-c. 558)
Isidorus of Miletus (c. 540?)
Eutocius of Ascalon (c. 550?)
Liu Zhuo (544-610)
Zhen Luan (Shuzun) (fl. 566)
Isidore of Seville (c. 560-636)

Hope you enjoy it, the last hurrah
For your assignments, write a couple lines about how awful the Roman Empire was.

Absolutely!

Ok guys, now that we know about absolute values, lets learn how to plot them on a number line.

Absolute Value

Earlier we talked about how to always think of absolute value as simply a numbers' distance from zero.

Now we will expand on this!

when are we ever gonna use this?!

For today lets just list the ways we've used math in our daily lives
This does not apply if you don't use money or computers.

Tools! For The Tool Box!

This is an important yet simple concept to grasp

http://www.khanacademy.org/v/absolute-value-1?p=Algebra%20I%20Worked%20Examples

An easy way to think of absolute value is to remember that when you are asked about the absolute value of a number, its asking how far away the number is from zero. So dont think of absolute value as simply removing a numbers' negative status.

GO GO!

Here is a good concept we'll need involving algebra

http://www.khanacademy.org/v/averages?p=Algebra

Averages is a tool you will most likely use for the rest of your life, whether its the average of your test scores to see how well you're doing or the average amount of money you'll be making in your new business.
The importance of this cannot be underestimated and its essential that you have a firm graps of it because things will get much harder going forward.

Timeline update

400 C.E.

Dominus of Larissa (fl. c. 450)
Proclus Diadochus (410-485)
Zhang Qiujian [Chang Ch'iu-chien] (c. 450?)
Zu Chongzhi (Wenyuan) [Tsu Ch'ung-chih] (429-500)
Eutocius of Ascalon (fl. c. 480)
Marinus of Sichem (Neapolis) (c. 480?)

The first two people on the list actually lived in the same region and developed a heated rivalry involving the works of Plato. When Proclus eventually won, Dominus left Athens and went back to Syria. You guys just dont know the fury of men until it involves mathematics!

Back into it

Here we go!
We are going to move further into equations, once you have a firm basis in this we can move on.
This is very critical to learn as we will need it when we begin graphing ::GASP::

http://www.khanacademy.org/v/solving-equations-2?p=Algebra%20I%20Worked%20Examples

Its time to step it up, please continue emailing (personal email) me any questions and I will continue clarifying further. We have a very good discussion going and it will get more complicated as we continue.

Bane

We need one more concept before we get back into algebra.
The following is what many students believe is the bane of their mathematical existence, this is what gave students nightmares before algebra: Lowest common multiple!

Round 1: Fight!

http://www.khanacademy.org/v/least-common-multiple?p=Arithmetic

Break is over

300 B.C.E.

Pappus of Alexandria (fl. c. 300-c. 350)
Serenus of Antinopolis (c. 350)
Pandrosion (c. 350)
Theon of Alexandria (c. 390)
Martianus Capella (c. 365-440)
Synesius of Cyrene (c. 370-c. 413)
Hypatia of Alexandria (c. 370-415)

Alright class, final timeline update before we get back to to the really fun stuff!

Chinese contribution

200 B.C.E

Diogenes Laertius (c. 200)
Liu Hong (fl. 178-187)
Wang Fan (217-257)
Diophantus of Alexandria (c. 250?)
Sun Zi (c. 250?)
Zhao Shuang (Jun Qing) (c. 260)
Liu Hui (c. 263)
Porphyry (c. 234-c. 305) (Malchus the Tyrian, Porphyrius)
Anatolius of Alexandria (fl. c. 269)
Sporus (c. 280)
Iamblichus (c. 250-c. 350)
Xiahou Yang (c. 350?)

This is a golden era for the Chinese and although they wont make such large contributions as this in the future (so far) it marks a beginning where the Chinese never let up on their contributions to not only math, but science as well.

In fact, recent studies have shown a large part of scientifically peer reviewed papers being published now are actually Chinese.
http://articles.cnn.com/2011-03-29/world/china.world.science_1_china-output-papers?_s=PM:WORLD

The article mentions how the US is still ahead, but that it may be reaching an apex. This is the price the US will pay for having a large portion of its populance remember the roster of their favorite sports teams or the cast of their favorite TV shows rather than the names and the contributions of great people.

Timeline Update

100 C.E.
Balbus (fl. c. 100)
Menelaus of Alexandria (c. 100 CE)
Nicomachus of Gerasa (c. 100)
Zhang Heng (78-139)
Theon of Smyrna (c. 125)
Ptolemy (Claudius Ptolemaeus) (c. 100-c. 170)
Marinus of Tyre (c. 150)
Nehemiah (c. 150)
Apuleius of Madaura (Lucius Apuleius) (c. 124-c. 170)

You may have noticed I am using B.C.E. and C.E, as in Before Common Era and Common Era
While its not new, its much more popular now.
Its good to move away from religion based historical periods, now while this change may indirectly still be linked to christianity its a step in the right direction.

Leveling up!

Ok guys, looks like most of you think its pretty easy, so lets turn it up a notch

http://www.khanacademy.org/v/level-2-exponents?p=Pre-algebra

Side Quest

Its not exactly algebra but you need to know this before we continue with our algebra journey

http://www.khanacademy.org/v/level-1-exponents?p=Pre-algebra

Before

We'll take a break from algebra for a bit to focus on a concept that will be used a lot while learning algebra.
Negative numbers. Yes, there are things less than zero !
Amazing isnt it! Kinda like your bank account being negative 25 dollars because you were charged an overdraft fee. Now you will need 25 dollars just to make it back to zero dollars! Capitalism at its finest.

Lets get started. First adding and subtracting negative numbers

http://www.khanacademy.org/v/adding-subtracting-negative-numbers?p=Pre-algebra

Second: multiplying and dividing negative numbers

http://www.khanacademy.org/v/multiplying-and-dividing-negative-numbers?p=Pre-algebra

Forward March!

Thats it!

1 C.E.
Theodosius of Tripoli (c. 50? CE?)
Pamphila (c. 60 CE)
Heron of Alexandria (fl. 62 C.E.)

Yup, needless to say humanity was doing other things at this time rather than focusing on math.
History shows that whatever they were doing, it was nothing important.

What are the chances?

Now that we got a foothold in algebra, we can dive into probability.
There are these people called actuaries, they mostly work for insurance companies and are about as close as you can get to real fortune tellers. They are paid about 80,000 USD just to start. They are able to calculate how likely something bad is going to happen to you and based from those calculations your premiums will be figured out.
Now while the math involved in that job is a far cry from what youre about to learn, they had to take this same exact lesson.

http://www.khanacademy.org/v/probability--part-1?p=Probability

Level up!

Alright guys, Im glad youre all still with me. Its gonna get a bit rougher
Remember, Fear is the Mindkiller

http://www.khanacademy.org/v/equations-2?p=Algebra

A new challenger appears!

Today is a great day, we will be learning a concept that will stay with you for the rest of your academic life and beyond!
Algebra: from the Arabic Al meaning hard and gebra meaning as hell. (j/k)

http://www.khanacademy.org/v/simple-equations?p=Algebra

Math Level: Grade 5

Division Final Form!

The final boss form of division: Dividing Decimals!
Attack with courage, remember your training, and you will make it back alive!
http://www.khanacademy.org/v/dividing-decimal?p=Arithmetic

Picking it up

200 B.C.E.
Diogenes Laertius (c. 200)
Liu Hong (fl. 178-187)
Wang Fan (217-257)
Diophantus of Alexandria (c. 250?)
Sun Zi (c. 250?)
Zhao Shuang (Jun Qing) (c. 260)
Liu Hui (c. 263)
Porphyry (c. 234-c. 305) (Malchus the Tyrian, Porphyrius)
Anatolius of Alexandria (fl. c. 269)
Sporus (c. 280)
Iamblichus (c. 250-c. 350)
Xiahou Yang (c. 350?)

The Chinese join the fray!
Now while this isnt the first instance of Chinese contributors to mathematics, it is the biggest!
This great trend continues for hundreds of years. When all humans have a chance of contributing to something, awesome things can happen.

It gets worse

Another update for the timeline, I think we can all appreciate just how bad it is that the entire human race only had six humans contribute to mathematics over the course of 100 years.

100 B.C.E.
Zenodorus (c. 100?? BCE?)
Posidonius (c. 135-c. 51)
Marcus Terentius Varro (116-27)
Zeno of Sidon (c. 79 BCE)
Geminus of Rhodes (fl. c. 77 BCE)
Cleomedes (c. 40? BCE?)

Part of this

This is important as we get into fractions
http://www.khanacademy.org/video/equivalent-fractions?playlist=Arithmetic
Have no fear!

Level 4

Super Saiyan Level 4 division!
http://www.khanacademy.org/video/level-4-division?playlist=Arithmetic
Final stop before we expand our horizons again!

Downhill

200 B.C.E.
Dionysodorus of Amisus (c. 200?)
Diocles of Carystus (fl. c. 180)
Hypsicles of Alexandria (fl. c. 175)
Hipparchus of Nicaea (c. 180-c. 125)
Umaswati (c. 150)

It’s another slow century and it stays this bad for a couple hundred years.
In this time period, Mathematical advancement is still concentrated in the Mediterranean region

More

Second level division, numbers get longer this time, stick with it!

http://www.khanacademy.org/video/division-2?playlist=Arithmetic

repetition is key!

We Move

300 B.C.E.
Autolycus of Pitane (fl. c. 300)
Euclid (fl. c. 295)
Aristarchus of Samos (c. 310-230)
Archimedes of Syracuse (287-212)
Philo of Byzantium (fl. c. 250)
Nicoteles of Cyrene (c. 250)
Strato (c. 250)
Persius (c. 250?)
Eratosthenes of Cyrene (c. 276-c. 195) 
Chrysippus (280-206)
Conon of Samos (fl. c. 245)
Apollonius of Perga (c. 260-c. 185)
Nicomedes (c. 240?) 
Dositheus of Alexandria (fl. c. 230) 
Perseus (fl. 300-70 B.C.E.?)

So begins a continual downward spiral in the number of contributors to mathematics, if you know your history you will know that the Roman Empire begins expanding its tentacles outward from the Italian peninsula. It shouldn’t need to be pointed out that their interest in Math and Science was not exactly Greek like

And so it begins..

A new concept, division!

http://www.khanacademy.org/video/division-1?playlist=Arithmetic

This is very useful and is one of the four basic math methods next to addition, subtraction and multiplication.

Once this is mastered we can move on to the great beyond!

Timeline Update

Unfortunately this is the largest number of names we will have for a few hundred years until the Arabs make their contributions. It all goes down hill from here for a number of reasons

Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?) 

Archytas of Tarentum (of Taras) (c. 428-c. 347) 

Plato (427-347)

Theaetetus of Athens (c. 415-c. 369) 

Leodamas of Thasos (fl. c. 380) 

Leon (fl. c. 375) 

Eudoxus of Cnidos (c. 400-c. 347)

Callipus of Cyzicus (fl. c. 370) 

Xenocrates of Chalcedon (c. 396-314) 

Heraclides of Pontus (c. 390-c. 322) 

Bryson of Heraclea (c 350?) 

Menaechmus (c. 350) 

Theudius of Magnesia (c. 350?) 

Thymaridas (c. 350) 

Dinostratus (fl. c. 350) 

Speusippus (d. 339)

Aristotle (384-322) 

Aristaeus the Elder (fl. c. 350-330) 

Eudemus of Rhodes (the Peripatetic) (fl. c. 335) 

Lattice Multiplication

There is a reason they dont really teach this in schools as it is a bit clumsy, not always applicable and would require us to re-teach math basics in some areas.
http://www.khanacademy.org/video/lattice-multiplication?playlist=Arithmetic

Its a great tool in many situations though!

Continue

Now for the next level
http://www.khanacademy.org/video/multiplication-6--multiple-digit-numbers?playlist=Arithmetic
one more step after this

Lesson update

Double digits now!
http://www.khanacademy.org/video/multiplication-4--2-digit-times-1-digit-number?playlist=Arithmetic
These are the basics guys, this must be learned before you continue!

Timeline update

400 B.C.E.

Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?)
Archytas of Tarentum (of Taras) (c. 428-c. 347)
Plato (427-347)
Theaetetus of Athens (c. 415-c. 369)
Leodamas of Thasos (fl. c. 380)
Leon (fl. c. 375)
Eudoxus of Cnidos (c. 400-c. 347)
Callipus of Cyzicus (fl. c. 370)
Xenocrates of Chalcedon (c. 396-314)
Heraclides of Pontus (c. 390-c. 322)
Bryson of Heraclea (c 350?)
Menaechmus (c. 350)
Theudius of Magnesia (c. 350?)
Thymaridas (c. 350)
Dinostratus (fl. c. 350)
Speusippus (d. 339)
Aristotle (384-322)
Aristaeus the Elder (fl. c. 350-330)
Eudemus of Rhodes (the Peripatetic) (fl. c. 335)

As you can see the word is out and lots of people are now joining the party

It just got real

Multiplication!
http://www.khanacademy.org/video/basic-multiplication?playlist=Arithmetic
Math Level: Grade 4
Please do try to keep up!

Timeline update

500 B.C.E.

Katyayana (c. 500) 

Nabu-rimanni (c. 490) 

Kidinu (c. 480) 

Anaxagoras of Clazomenae (c. 500-c. 428) 

Zeno of Elea (c. 490-c. 430) 

Antiphon of Rhamnos (the Sophist) (c. 480-411)  

Oenopides of Chios (c. 450?) 

Leucippus (c. 450) 

Hippocrates of Chios (fl. c. 440) 

Meton (c. 430) 

Hippias of Elis (fl. c. 425) 

Theodorus of Cyrene (c. 425) 

Socrates (469-399) 

Philolaus of Croton (d. c. 390) 

Democritus of Abdera (c. 460-370) 

History is doing a much better job at recording the names of the people who contributed to math, its important to note that hard drives are still not available in this time period

History Lesson 2

OK class, here are some names you should get to know
This is about 600 B.C.E. on the timeline

Thales of Miletus
Apastamba
Anaximander of Miletus
Pythagoras of Samos (yes that Pythagoras)
Anaximenes of Miletus
Cleostratus of Tenedos

This is about the time when many contributions were made to mathematics, previously we've had one person make some kind of a contribution. Again, math was not high on ancient mans list of things to do

Now the opposite

Here is the reverse concept!
http://www.khanacademy.org/video/basic-subtraction?playlist=Arithmetic

Email me more questions or comments if you have any

Math Level: Grade 3

Level 3

Math Level: Grade 2
http://www.khanacademy.org/video/addition-3?playlist=Arithmetic

I appreciate the emails telling me how easy this is, so there is nothing to worry about here either

Keep it goin

Lets continue
http://www.khanacademy.org/video/level-2-addition?playlist=Arithmetic
Make sure to keep up.

Some people can tell you where they stared having trouble with math. Its not here, so dont worry

Indian Contribution

Baudhayana 700 B.C.E.

This is a good book if you are interested in the history of math


Bourbaki, Nicolas (1998), Elements of the History of Mathematics, Berlin, Heidelberg, and New York: Springer-Verlag, 301 pages, ISBN 3540647678, http://www.amazon.com/Elements-History-Mathematics-Nicolas-Bourbaki/dp/3540647678/ .

I am going to continue pointing out the contributions made by certain peoples to mathematics as we go on.
Its good to note that for a civilization to make a contribution to math, it must satisty a number of other requirements first. Among them is not have a starving populace and not be wiped out by war. It is a bad work enviroment

Lets get it started

What some math looked like at that time.
http://www.khanacademy.org/video/basic-addition?playlist=Arithmetic

This was "math" for the greater part of a millenium, there was simply no need for any of even the most basic functions in math. 1 goat + 1 goat, ok our village has 2 goats.

Math level (American): First grade
Going forward I wont point out that I will be useing the American educational system.

First Prime

Ahmes/Ahmose writes the Rhind Mathematical Papyrus around 1650 BCE in Egypt; the first person in recorded history to have his name tied to mathematics


Note: This blog has been set up to create a near linear explanation of how we can go from simple addition to algebra to the highest levels of math. It was created for a group of a few dozen people who have some interest in math, but I hope to make a few freinds along the way and re-introduce people to math