AI News, I am pursuing a PhD in machine learning. How do I improve my math skills?

I am pursuing a PhD in machine learning. How do I improve my math skills?

Unfortunately, those ideas were just my feelings and opinions and that’s why they were fundamentally wrong — I cannot build anything from the basis of my feelings.

Implementing those ideas seemed too complex to achieve and eventually I couldn’t accomplish the goal I was setting to myself.

This is the moment when your ideas come to alive: first they live in the world of mathematics, but eventually you can touch them.

You can think “what if the world would be like this”, and then you can prove that your ideas are actually working from that assumption.

It only takes time but the benefit is enormous: your ideas are not just ideas, they are actually working!

If you did a good job and your proof is complete, the only thing left to do is to change the world to be like you’ve assumed it to be.

And don’t take it personally, if you are right you’re right — it’s not a matter of opinion.

education.govt.nz for Parents Practical information about education for parents and carers

You can help your child's learning every day, by supporting and encouraging them and being excited by their learning.

Reading at home should be fun and easy – something you both look forward to - a time for laughter and talk.

Make reading: Here's some tips - If your child is stuck on a word wait a few seconds, give them a chance to think.

Involve your child in: Here's a tip - use lots of mathematics words as your child is playing to develop their understanding of early mathematics (eg 'over', 'under', 'first, second, third', 'round', 'through', 'before', 'after').

Get together with your child and: Here's a tip - being positive about mathematics is really important for your child’s learning – even if you didn’t enjoy it or do well at it yourself at school.

Help your child to: Here's a tip - being positive about mathematics is really important for your child’s learning – even if you didn’t enjoy it or do well at it yourself at school.

If you or your child starts to feel stressed by what they’re reading, take a break and read the rest of the story aloud yourself – keep it fun.

Help your child to: Here's a tip - being positive about mathematics is really important for your child’s learning – even if you didn’t enjoy it or do well at it yourself at school.

Here's some tips - Keep the magic of listening to a good story alive by reading either made up, retold or read-aloud stories to your child – with lots of excitement through the use of your voice!

To do this your child will use their knowledge of words and word patterns (eg prefixes, suffixes and root words) to help build meaning.

Help your child to: Here's a tip - being positive about mathematics is really important for your child’s learning – even if you didn’t enjoy it or do well at it yourself at school.

Here's a tip - keep the magic of listening to a good story alive by reading either made up, retold or read-aloud stories to your child – with lots of excitement through the use of your voice.

Help your child to: Here's a tip - being positive about mathematics is really important for your child’s learning – even if you didn’t enjoy it or do well at it yourself at school.

Here's a tip - keep the magic of listening to a good story alive by reading either made up, retold or read-aloud stories to your child – with lots of excitement through the use of your voice!

Let your child see you enjoying reading – whether it’s the newspaper, a magazine, a comic, a cook book or a novel.

Encourage your child to write: Here's a tip - keep writing fun and use any excuse you can think of to encourage your child to write about anything, anytime.

Help your child: Here's a tip - being positive about maths is really important for your child’s learning – even if you didn’t enjoy it or do well at it yourself at school.

Involve your child in: Get together with your child and: Here's some tips - mathematics is an important part of everyday life and there are lots of ways you can make it fun for your child.

Here's a tip - keep the magic of just listening to a good story alive by reading either made up, retold or read-aloud stories – with lots of excitement through the use of your voice.

Show your child that you write for lots of reasons, eg replying to an email, writing a shopping list, invitation or letter, writing for your work or your own study.

Help your child to: Here's a tip - being positive about mathematics is really important for your child’s learning – even if you didn’t enjoy it or do well at it yourself at school.

Let your child see you enjoying reading – whether it’s the newspaper, a magazine, a comic, a cook book or a novel.

Show your child that you write for lots of reasons, eg replying to an email, writing a shopping list, invitation or letter, writing a story about your early life for your child to read.

Get together with your child to: Here's a tip - make writing fun and use any excuse you can think of to encourage your child to write about anything, anytime.

Involve your child in: Here's a tip - talk with your child’s teacher to understand what they are learning in mathematics and what the learning is in the homework they’re doing.

Get together with your child and: Here's a tip - being positive about mathematics is really important for your child’s learning – even if you didn’ t enjoy it or do well at it yourself at school.

Why Math Is the Best Way to Make Sense of the World

When Rebecca Goldin spoke to a recent class of incoming freshmen at George Mason University, she relayed a disheartening statistic: According to a recent study, 36 percent of college students don’t significantly improve in critical thinking during their four-year tenure.

But if you look closer, Goldin told her bright-eyed audience, you’ll find a different message: “Turns out, this third of students isn’t taking any science.” Goldin, a professor of mathematical sciences at George Mason, has made it her life’s work to improve quantitative literacy.

In 2004, she became the research director of George Mason’s Statistical Assessment Service, which aimed “to correct scientific misunderstanding in the media resulting from bad science, politics or a simple lack of information or knowledge.” The project has since morphed into STATS (run by the nonprofit Sense About Science USA and the American Statistical Association), with Goldin as its director.

In conversation, however, it quickly became apparent that the bridge between these two selves is Goldin’s conviction that mathematical reasoning and study is not only widely useful, but also pleasurable.

At the dinner table, my dad, who is a physicist, would pull out some weird puzzle or riddle that sometimes only took a minute to solve, and other times I’d be like, “Huh, I have no idea how that one works!” But there was an overall framework of joy around solving it.

This comes about when you’re interested in things like our universe, where the Earth is rotating, and it’s also rotating around the sun, and the sun is in a larger system that is rotating.

This is useful because if you’re trying to solve equations, and you know you have symmetries, you can essentially find a way mathematically to get rid of those symmetries and make your equations simpler.

When I first joined what became STATS, it was a little bit more “gotcha” work: looking at how the media talks about science and mathematics and pointing out when someone has gotten it wrong.

We found pretty early in our work that there was this huge gap of knowledge and education: Journalists were writing about things that had quantitative content, but they often didn’t absorb what they were writing about, and didn’t understand it, and didn’t have any way to do better because they were often on really tight timelines with limited resources.

They could be as simple as “I don’t know how to calculate this percentage,” or they could be pretty sophisticated things, like “I’ve got this data, and I want to apply this model to it, and I just want to make sure that I’m handling the outliers correctly.” The other really cool thing that we do is, we go to individual news agencies and offer workshops on things like confidence intervals, statistical significance, p values, and all this highly technical language.

What you can answer is the question of whether women who take hormones whom you enroll in your study — those specific women — have an increase or decrease in, say, heart disease rates or breast cancer rates or stroke rates compared to a control group or to the general population.

Partly our goal is to help change the culture of journalism so that people recognize the importance of using quantitative arguments and thinking about quantitative issues before they come to conclusions.

We want to arm journalists with a certain amount of rigor in their thinking so they can challenge a scientist who might say, “Well, you just don’t understand my sophisticated statistic.” There’s a lot of value in giving reporters the tools to develop their sense of quantitative skepticism so that they’re not just bullied.

I think that the current president is also causing a lot of reflection on what we mean by facts, and in that sense journalists maybe think of it as more important in general to get the facts right.

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

5 Things You Need To Know About The Future Of Math

Keith Devlin: To most people, mathematics means applying standard techniques to solve well defined problems with unique right answers.

By and large, most people outside mathematics did not experience the change until the rapid growth of the digital age in the last twenty years.

With cheap, ubiquitous computing devices that can do all of the procedural mathematics faster and more accurate than any human, no one who wants – or wants to keep – a good job can now ignore that shift from the old “application of known procedures” to new emphasis on creative problem solving.

Keith Devlin:When today’s parents were going through the schools, the main focus in mathematics was on mastery of a collection of standard procedures for solving well-defined problems that have unique right answers.

Suddenly, in a single generation, mastery of the procedural math skills that had ruled supreme for three thousand years has become largely irrelevant.

Jordan: But we’ve all seen statistics that show STEM (science, technology, engineering, math) skills are in high demand.

Keith: It’s still the case that math gets you jobs, but the skill that is in great demand today, and will continue to grow, is the ability to take a novel problem, possibly not well-defined, and likely not having a single “right” answer, and make progress on it, in some cases (but not all!) “solving” it (whatever that turns out to mean).

The problems we need mathermatics for today come in a messy, real-world context, and part of making progress is to figure out just what you need from that context.

Keith:In all four offerings of my mathematical thinking MOOC to date, I have had as students, engineers with years of experience who suddenly found themselves out of a job when their employers replaced them with software systems (or sometimes overseas outsource services).

Jordan:So you're not only saying that technology renders basic procedural mathematics skills obsolete, you're also suggesting that it offers new forms of dynamic representation?

What I and a small number of other math learning game developers are doing, but most are not, is viewing the game as a representation of mathematics that replaces the traditional symbols with one that takes advantages of the many different affordances that video game technology offers, particularly tablet screens.

Today, study of the symbolic representation can be postponed until after the student has mastered the basic mathematical thinking in a more efficient way.

Keith:In today’s world, where our Cartesian-based sciences and technologies play such a huge role in our lives and our societal structures, it is just as important to make people aware of the inherent limitations of mathematics as of its powers.

Just as we have made great progress in the natural sciences and engineering, so too other researchers have made great strides in the sciences of the mind and in the social, psychological, and learning sciences.

It was after working with (actually, mostly listening to) leading human scientists, and philosophers who consider those issues, that I was forced to reassess the role that mathematics can play in the human sciences.

How to Develop a Mindset for Math

Math uses made-up rules to create models and relationships.

In 1000 years we'll have a system that makes decimal numbers look as quaint as Roman Numerals ('By George, how did they manage with such clumsy tools?').

The Romans would consider zero and fractions strange, but it doesn't mean 'nothingness' and 'part to whole' aren't useful concepts.

Fractions (1/3), decimals (.234), and complex numbers (3 + 4i) are ways to express new relationships.

Even then, negative numbers may not exist in the way we think, as you convince me here: You: Negative numbers are a great idea, but don't inherently exist.

So the actual number I have (-3 or 0) depends on whether I think he'll pay me back.

We've created a 'negative number' model to help with bookkeeping, even though you can't hold -3 cows in your hand.

(I purposefully used a different interpretation of what 'negative' means: it's a different counting system, just like Roman numerals and decimals are different counting systems.) By the way, negative numbers weren't accepted by many people, including Western mathematicians, until the 1700s.

want to share what I've discovered, hoping it helps you learn math: Sure, some models appear to have no use: 'What good are imaginary numbers?', many students ask.

The use of imaginary numbers is limited by our imagination and understanding -- just like negative numbers are 'useless' unless you have the idea of debt, imaginary numbers can be confusing because we don't truly understand the relationship they represent.

I want to cover complex numbers, calculus and other elusive topics by focusing on relationships, not proofs and mechanics.

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