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## #1 Re: Dark Discussions at Cafe Infinity » What worldy occurrences can we think of in terms of mathematics? » 2013-10-01 12:52:00

@bobbym

I understand now. One point i'm trying to make is that 50/50 doesn't mean that's the way it will turn out. For example I have seen a coin flip to give 6 heads and 2 tails in 8 flips. That is 75:25 heads to tails. However the more you flip the more the results usually even out to around 50/50 overtime. Just because something has a high probability doesn't mean it will happen. The result is unpredictable each time. We are just guessing the likelihood based on some data. In this case there is a 1 or the other option so we say they both have an equal chance.

Likewise we might say a person going to university has a higher chance of being successful than a drop out but some drop outs become millionaires even though the probability is bad. However maybe there was something peculiar about the certain drop out that was not factored in. What i'm trying to say is we guess the probability based on what we know. There are two sides of a coin so we say 50/50 chance which makes sense. However we are ignorant of a lot about the universe. There may be more factors in every coin flip than we know. Not including what I stated before. The coin flip concept has only two outcomes so is very simple. Now if you try to take something like an economy and apply probability then God help you. There are so many variables. Nevertheless i'm sure people use probability to invest and such.

You could easily take statistics of people buying homes and finishing the mortgage payments over 30 years. Then see what factors stop people finishing the payments. Then assign some percentage of probability to each candidate based on their answers to questions. Then decide whether you'll give them insurance and how much you'll charge. I'm sure this is already done by people.

It is all really educated guessing in my opinion. Though whether they have sufficient information is up for debate. With simple casinos probability works because there aren't many variables except for card counting, hi end cheating, or something like that. When you use probability in fields with more variables then probability can fail miserably.

## #2 Re: Dark Discussions at Cafe Infinity » What worldy occurrences can we think of in terms of mathematics? » 2013-10-01 08:52:04

The majority of people see math as useless.
That is true, but the majority is almost always wrong. As you mention later, people tend to follow the majority, the trend, but it is rarely the best way.

You asked a lot of questions and only a few of them can be answered. For one thing when we speak of probability of a coin toss we are speaking about perfect coins that have a 50-50 chance. Real coins are biased.

The rules of probability have been worked out a long time ago. The important thing is they work.

Can you elaborate on this? I'm not sure if I understand correctly. Do you mean a perfect coin is an abstract concept which doesn't exist in the real world, yet probability theory works in the real world? Or do you mean something else?

## #3 Dark Discussions at Cafe Infinity » What worldy occurrences can we think of in terms of mathematics? » 2013-10-01 04:31:30

daijoubu
Replies: 5

I have been thinking about this for a while. The majority of people see math as useless. Beyond arithmetic, fractions, ratios & percentages and basic geometry there is nothing useful for the average person. Anything to do with algebra or beyond is almost exclusively used by people in Science, Technology, Engineering and Mathematics itself.

So what way can you use algebra in our daily lives? A friend of mine used it at a restaurant when the bill came. So she could work out who owes what, since we didn't pay ourselves. I can't think of many other ways to use math in real life. You can use some probability when gambling. I have used basic algebra when making the most basic of programs.

I was thinking about probability the other day. How we seem to make it up. A coin flip we say has a 50/50 chance, but we don't know this. It just seems logical that two options would have a 50/50 chance if there's no other known variables. We rarely ever get an equal amount of heads and tails in the real world. Probability is just an educated guess in my opinion. It's just the likelyhood from what we know. For a simple coin toss i'm sure it would be wiser to factor in the person flipping the coin, how they flip it, and what head the place it on before they flip.

Nevertheless probability generally works over time. If there is a 75% win on blue, but 25% win on red, then any logical person would choose blue over an over. Overtime they will win more than lose which will have a compounded affect. Unless they had some better way to predict each outcome every time. Now imagine for each decision in life we had some way of knowing the probability. If we followed the option with the highest probability each time then over the course of our lives the benefits would add up. Though we can't exactly give something a probability because it would be a guess. However if you could narrow down the most contributing factors and gather statistics then this would be possible.

I think on a subconscious level people weigh their options like this anyway. You might avoid going to an area because of the high crime rate. People put their children in schools with high success rates. Now imagine you had statistics and could predict simple things as which degrees are most likely to get a job that pays x amount. What attributes are most desired by these types of women. You would simply follow probabilities which give you a better chance in life. Of course that is hard to quantify.

What Can anyone think of any creative ways to use math in the real world?

## #4 Re: Introductions » Here to learn » 2013-09-29 12:14:11

@ bob bundy prove that 'half' the sum of 4 consecutive numbers is odd.

## #5 Re: Introductions » Here to learn » 2013-09-28 11:50:27

No I have never seen that site before. The questions seem slightly more difficult than what i'm used to but manageable. Thank you for the link. I am just going to practice these sites for a few months then lol.

Do you know anymore? I also would like to know of websites with practice questions with solutions, tutorials, or information that goes into depth. It may seem counter intuitive but the more information i'm bombarded with about a topic, the easier it is for me to understand and remember.

## #6 Re: Introductions » Here to learn » 2013-09-28 11:26:52

basic algebra, geometry, trig or precalculus. I'm basically in between GCSE and AS level math in the UK so I wont be able to deal with the higher level topics. The problems on exams I have encountered don't last long and aren't really challenging as long as you know the formulas. You don't have to think much and just follow the rules.

I am interested in basic proofs but never really understood them that well. We moved from demonstration to basic proof but the teachers never really explained it well.

prove that the sum of 4 consecutive numbers is odd.

n
2n = even
2n + or - 1 = odd

(n-1)+n  +(n+1)  + (n+2)

1/2(4n+2)

2n+1
therefore 2n+1 is odd.

I'm interested in proofs but barely know the basics. I am going to look at proof by induction soon but proofs seem more difficult to understand than anything I have done so far.

## #7 Re: Introductions » Here to learn » 2013-09-28 11:14:35

Can you suggest any fun parts of maths that aren't beyond pre calculus?

## #8 Introductions » Here to learn » 2013-09-28 10:45:41

daijoubu
Replies: 13

Hello i'm daijoubu. I'm currently at an elementary maths level but what to get to the point where I can solve olympiad problems. I hope that you can help me and I can help you.