The MATH Thread | Realm of Thought | PinoyExchange

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How to get better at Math?

For now, to supplement my online programming course, I took an online algebra course at Edx which is not part of the curriculum. I am also taking some baby steps in Calculus. My aim is to master foundational concepts so that I could tackle Discrete Mathematics, a type of Math that requires proving. I don't know yet how proving is connected to Computer Science. I am still thinking though if I have to get into a real university. I feel I learn much deeper in online lectures since I can repeat it again and again.

***

Here are fun problems:

A lily pad grows twice its size everyday. In 48 days, it filled an entire lake. How long would it take to cover half the lake?

I want to buy a shirt that costs P970. I asked P500 from mom, and P500 from dad. I finally bought the shirt and got a change of P30. I sent P10 to mom, and P10 to dad, and got P10 for myself. Therefore, I owe mom P490, I owe dad P490, a total of P980. Since I got P10, where is the other P10?

Hint: the problem above is more accounting than algebra. You can get it in no time.

2. Originally Posted by crocopie
How to get better at Math?

For now, to supplement my online programming course, I took an online algebra course at Edx which is not part of the curriculum. I am also taking some baby steps in Calculus. My aim is to master foundational concepts so that I could tackle Discrete Mathematics, a type of Math that requires proving. I don't know yet how proving is connected to Computer Science. I am still thinking though if I have to get into a real university. I feel I learn much deeper in online lectures since I can repeat it again and again.

***

Here are fun problems:

A lily pad grows twice its size everyday. In 48 days, it filled an entire lake. How long would it take to cover half the lake?

I want to buy a shirt that costs P970. I asked P500 from mom, and P500 from dad. I finally bought the shirt and got a change of P30. I sent P10 to mom, and P10 to dad, and got P10 for myself. Therefore, I owe mom P490, I owe dad P490, a total of P980. Since I got P10, where is the other P10?

Hint: the problem above is more accounting than algebra. You can get it in no time.
The lily filled half of the lake on the 47th day.

3. There is no missing P10.

Assets = Liabilities

Assets:
P970 - worth of shirt
P10 - cash
-----
P980

Liabilities:
P490 - mom
-------
P980

4. Originally Posted by Ateo
The lily filled half of the lake on the 47th day.
very smart!

5. I just watched Gilbert Strang's first video lecture on Calculus. Magulo pa para sa akin, but the main takeaway for me is this:

The Derivative is the slope of a graph. The Integral is the area covered under a graph. What they do is measure changes that would take us from one function to the other.

Distance is the Integral of Velocity times Time because of the area covered under the graph. At constant speed it is one horizontal line.

Velocity is the derivative of Distance because if you measure the slope by dividing change of Distance by change of time, you get the velocity.

Yun muna..

6. Originally Posted by Ateo
There is no missing P10.

Assets = Liabilities

Assets:
P970 - worth of shirt
P10 - cash
-----
P980

Liabilities:
P490 - mom
-------
P980
dominic ikaw ba yan?

7. kids stuff...

test:

I have a pen,
I have an apple

8. Originally Posted by Jagon
kids stuff...

test:

I have a pen,
I have an apple

you draw a face on the apple. hey thats what kids would do!

9. Originally Posted by sophion
you draw a face on the apple. hey thats what kids would do!

"nyeheehhe, hey apple!"

10. If you would like to brush up your foundational algebra, this is a good site to start:

https://www.edx.org/course/college-a...g-asux-mat117x

It's a good start. Not too threatening yet very very vast. I suggest to get a notebook. And a cheat sheet, which you can get here:

http://tutorial.math.lamar.edu/pdf/A...heat_Sheet.pdf

I also found a short trig course here:

http://www2.clarku.edu/~djoyce/trig/

11. Originally Posted by crocopie
How to get better at Math?

For now, to supplement my online programming course, I took an online algebra course at Edx which is not part of the curriculum. I am also taking some baby steps in Calculus. My aim is to master foundational concepts so that I could tackle Discrete Mathematics, a type of Math that requires proving. I don't know yet how proving is connected to Computer Science. I am still thinking though if I have to get into a real university. I feel I learn much deeper in online lectures since I can repeat it again and again.

***

Here are fun problems:

A lily pad grows twice its size everyday. In 48 days, it filled an entire lake. How long would it take to cover half the lake?

I want to buy a shirt that costs P970. I asked P500 from mom, and P500 from dad. I finally bought the shirt and got a change of P30. I sent P10 to mom, and P10 to dad, and got P10 for myself. Therefore, I owe mom P490, I owe dad P490, a total of P980. Since I got P10, where is the other P10?

Hint: the problem above is more accounting than algebra. You can get it in no time.
First is an Exponential growth and decay problem..

Lastly, I love calculus also. Wait until you get to Calculus 2. That's where the fun starts.

12. if you Prove that 2 + 2 = 5 in 3 lines or less,

di na ako tatambay sa rot.

13. They say a family is well-off financially if annual tuition fees don't exceed 100% of monthly gross income. Things get difficult if it touches 200%.

Given that tuition fees go up at a VERY different rate from monthly gross income, how will the mathematical model look?

14. Crocopie,

Saan website ka nagaaral programming? free ba? gusto ko din kasi sana magstart programming lessons yung pinakabasic lang muna sana. Kaso yung mga website na nakikita ko puro for web development programming ata gusto ko sana yung pang basic lang muna. Pwede palink dito or pm?

15. Originally Posted by mousetraps
Crocopie,

Saan website ka nagaaral programming? free ba? gusto ko din kasi sana magstart programming lessons yung pinakabasic lang muna sana. Kaso yung mga website na nakikita ko puro for web development programming ata gusto ko sana yung pang basic lang muna. Pwede palink dito or pm?
Look for OSS Society by Github

16. Crocopie,

thanks sa info. nagstart na rin ako pinakabasic sa codeacademy.com hehe talagang yung pang zero knowledge sa coding. nagstart ako ngayon python then next ko java siguro parang yun kasi ang mga in demand at marami applications?

then after dito sa codeacademy try ko siguro yan oss society or itong sa harvard or MIT na online computer programming course. free din pero kung gusto mo makakuha certificate after you've finished the course meron bayad 90 dollars.. ang style para din yatang ganyan yung sa oss society na meron lectures pero dahil online eh papanoorin mo lang ata tapos meron problem sets and + projects din parang nakaenroll talaga dun sa course feeling harvard or MIT students tayo haha..

eto yung sa harvard: http://online-learning.harvard.edu/c...mputer-science

ayun goodluck sa atin lahat sana matuto tayo.

17. Week 6 is nakakabuwisit kung madalas offline ka. Since March ko pa ginagawa hindi ko pa maintindihan.

First of all, watch this video:

Now, if d = t^2 and dx/dt = 2t:

So if time is 3 seconds, distance must be 9 meters. Now the derivative must be 6 meters/sec (since 3 x 2 = 6)

If velocity is the derivative of distance, how come when I add the current distance from the current velocity (9 + 6),

I have to add +1 to get the distance of the next second? ( That is , 9 + 6 + 1 = 16 meters, 4^2 = 16 meters)

Where did the +1 come from?

Try other values of t seconds. The outcome would always be (d + dx/dt + 1) to get the distance of the next t.

19. Originally Posted by sophion
very smart!
Nakuha ko agad yung first problem. pero umikot talaga utak ko sa 2nd problem.

20. Originally Posted by crocopie
Now, if d = t^2 and dx/dt = 2t:

So if time is 3 seconds, distance must be 9 meters. Now the derivative must be 6 meters/sec (since 3 x 2 = 6)

If velocity is the derivative of distance, how come when I add the current distance from the current velocity (9 + 6),

I have to add +1 to get the distance of the next second? ( That is , 9 + 6 + 1 = 16 meters, 4^2 = 16 meters)

Where did the +1 come from?

Try other values of t seconds. The outcome would always be (d + dx/dt + 1) to get the distance of the next t.
To get the distance after a time, you have to plug in the value of time in the original equation d = t^2; hence,

at 4 sec
d = (4)^2
d = 16

at 5 sec,
d = (5)^2
d = 25

at 6 sec,
d = (6)^2
d = 36

You now see the pattern.

The problem with d + dx/dt + 1 is you can't add differing units. That's why in Physics, we learn conversion first. So don't worry about d + dx/dt + 1, just go back to the original equation and plug in the time, then you always get the distance covered at that time.

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