Liam Tran

Chapter 1:

Not everything is a line, we also need to think about nonlinear, an example: If we the government put the tax too low we wont have enought revenue or funding to do our business, but if we put it too high the cityzen won’t even bother working because all there money will be drained to pay tax. So when we say something without thinking we should ask how would this work out first

Chapter 2 Think in every way you can and focus on logic. Example: 0.99999999999… is close to one but not quite. But if we think of it this way— 0.3333333… is equal to 1/3. Multiply that be three we have 1. Multiply 0.3333333… by three we get 0.9999999…Does that mean 0.9999999999… is equal to 1?

In chapter three, “Everyone Is Obese,” of How Not to Be Wrong, Jordan Ellenberg explains how misapplying mathematical concep is like linear regression can produce misleading conclusions. It is always better to grasp the concept of a lesson in our own words than remembering all the examples but can’t do the equations it self

Chapter 4: an important rule in mathematical thinking is when you are field testing, try testing the same thing in different ways,if you get several different answers then there might be something wrong with the method.another thing thats in this chapter is thinking about ratios and probabilities, if a group with 10 people get one person injured and a group of 100 people with 10 people injured we cannot say that the 100 people group has a more injured rate. Also if we flip a coin 4 times and its all heads, our brain would think that it would be tails next.

Chapter 5:

The idea is percent changes often be tricky

Example: A politician claims a state created most national jobs — but that’s because they used percentages cleverly to make a story look better than the raw numbers say. As if he could say his state makes 300% more than the other state. But turn out the other state is smaller and he doesn’t mention that

Chapter 6:

Main idea: Strange patterns can happen by chance.

Example: people sees a ‘code’ in the Bible and thinks its some hidden secret. but turns out it is just a coincidence that we see a pattern in the Bible all though there is none

Chapter 7

The author talks about how science experiments can be wrong but sounds fancy and we tend to believe it. Such as and example where science said we can read the minds dead dish though a machine but turns put that is false and the sound/ electric waves is just normal

Chapter 8

Main idea: Use logic to rule out impossible ideas.

Example: Ellenberg shows how proofs by contradiction (arguing something is impossible because it leads to an answer that doesn’t make sense or doesn’t have a clear solution ) help mathematicians solve big problems like the gaps between prime numbers.

Chapter 9

Main idea: Be careful with scientific posts or similar things with unclarified source

Example: If researchers test many things and only report good ones, it can be fake. That’s how so-called discoveries get published by accident.

Chapter 10

The main idea is that we might have an thought but can change our minds if we recieve new information such as when we wake up and see no cloud we think its going to be a sunny day but the a few minutes later we see storm clouds and will assume its going to rain

Chapter 11

Main idea: understand risky games to help with successful results

Example: MIT students found a way to guarantee lottery profits by buying lots of different number combinations, lowering risk (variance) while the math stayed in their favor.

Chapter 12

Main idea: Don’t waste all your time avoiding tiny risk by waiting

Example: If you try to never miss a flight, you might waste all your life waiting early at airports – instead, math (utility) helps find a reasonable solution.

Chapter 13

Main idea is that we should spread the risk for errors evenly may help avoid critical damage to one part of our project

Example:

Gamblers buy ticket with each one clearly different than the others to get a higher chance of winning.

Chapter 14, 15

Main idea: Extreme or different than average results tend to average out.

Example: A business’s best performers often regress to the mean — the next year they’re closer to average. So last year’s star may not have stay that great. Or because the average is moving up. Another example children of tall parents might be tall but will be unlikely to be as tall that because genes will also head back to average.

Chapter 16

Just because two (or more) things are connected together doesn’t nessersary mean that one of them directly cause another and could be the other way around. We could say ice cream causes global warming and in a way it does but it does not directly cause it

Chapter 17

Main idea: Votes and multiple choices type of answers don’t always lead to a clear “true opinion.”

Example: Voting systems like majority rule can denythemselves everyone could prefer A over B, B over C, and C over A in a cycle. Or some senarios there could be no good enough answer

Chapter 18

Main idea: Some math ideas can exist even if they seem weird.

Example: Non-Euclidean geometry (different shapes of space can exist in form of ) shows math isn’t just rules you memorized in school — it can explore completely new kinds of worlds or imagination.