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  #1  
Old 07-02-14, 11:35 PM
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Question Fastest route to Maths & Science Catchup

Really interested on some feedback on this one from anyone that can help please.

My school career ended when I was kicked out shortly before my 15th birthday due to the usual litany of "crimes" in a smart but undiagnosed kid with ADHD. At the time I was academically ranked in the lowest percentile, deeply depressed and ashamed, result being that I hadn't listened to a word said in class for a very long time. Long story short, I am missing yeeeeeeeeeeeeeeaaaarrs of basic education .. probably not uncommon amongst our folk?

I had the lucky fortune to have someone take me under their wing in my late teens and convince me I was actually bright and ended up going to uni and getting a business / computing degree in my 20s and psych degree in my 30s. Both were gained through the "brute force" method of rote learning and studying probably 10 times as hard as anyone else (have since repeatedly read this is pretty common for our folk). One of my big passions in psych is neuro however I had to "brute force" again, literally hours and hours and HOURS of rote learning stuff because I didn't have the basic underpinnings in chemistry and biology. So i.e., I would be at the point where I would be explaining g protein's activating enzymes etc .. without knowing what was really going on underneath it all.

I'm now 43, was only diagnosed about 18 months ago with ADHD, and it's finally time to go back and gain this knowledge (sigh - if only we could upload the data). I'm starting a PhD next year (ADHD / Mindfulness / Neuro / Biofeedback - still broad and culling) and I really want to get a decent handle on this stuff before I get started. For the last almost 12 months I've been reading solidly in the associated literature and there's still so much of it I can't quickly engage with . I'm also really interested in the genetic / epigenetic world but can only get so far because I'm missing so much basic knowledge. It's too big an area for me to master by "brute" force - while that method may "work" at undergrad level, it's simply regurgitative (my word) learning, rather than productive if you know what I mean. I've hit my ceiling without getting some of the basics .. but which?

So what I'm seeking is some sort of fast track method to get up to speed as quickly as possible. Each time I ask someone who's in a science related field they respond with a lot of "just's" e.g., "just do an organic chemistry unit" but then I go and look up organic chemistry and it will have pre-reqs of e.g., BIO101 / CHEM101 and then they both have pre-reqs of all sorts of maths which I didn't do.

A couple of months ago I started an online maths course here in Australia and spend a short time each day on this and am about to graduate from 6th grade LOL. High school maths next .. but how much of it do I need? I'm a sole parent and time is something I can't afford to waste.

Does anyone know of any sort of info hierarchy of maths and science and how they all fit together?

What's the wisest way to approach this?

Coursera have some intro courses in science but I can't untangle my way through all the different subtypes because I don't know what many of them are.

Thanks for any advice on this.
Ruby
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Old 07-03-14, 12:09 AM
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Re: Fastest route to Maths & Science Catchup

Hi Ruby,

Can you please tell me what kind of mathematics you need?

A short hierarchy from the top of my head:

Basic skills:

High School Maths

Slightly more advanced (and probably a prerequisite for the topics below)

Pre calc
Calculus
Linear Algebra

More advanced:

Probability, Statistics, Differential Equations, Discrete Mathematics
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Old 07-03-14, 01:24 AM
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Re: Fastest route to Maths & Science Catchup

You need Algebra and Trigonometry at High School Level, because you will use these in Calculus and Statistics later on.

You can safely skip all Euclidean Geometry beyond the basic primary school stuff.

At college level, you will need two semesters worth of Calculus, and a single course in Probability and Statistics. You will also need elementary** linear algebra and elementary** differential equations. You can safely skip discrete maths.

Texts I reccomend:

1. Precalculus Math by Sobel and Lerner <-- This book has all the HS Algebra and Trig you need as well as Elem. Matrix Algebra and Probability. You should study this entire book.

2. Calculus by Stewart <-- You should study Chapters 1 - 7 pn univariate calculus, chapters 9 and 17 on elem. differential equations and the first few subsections of chapters 14 and 15 on multivariate calculus.

3. Managerial Statistics by Keller - Intended for Commerce students but a good book as it doesn't go into the unnecessary theoretical waffle that those intended for Scientists do. The first 14 chapters should be adequate.

Hope this helps
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Old 07-03-14, 06:36 AM
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Re: Fastest route to Maths & Science Catchup

Previous posts have given the order of pre-requisite maths accurately.

I think this is a good all round lecture series (about 40 lectures) on youtube which covers college algebra well (seems to cover mathematics from high school level up to starting calculus) and is in a different format than the usual 'lecturer in front of a blackboard' type which you may find helpful. Don't get disheartened if you are not quite up to this level yet as it just means that you may have to backtrack and do some earlier mathematics.



If you get through this then there is also a lecture series 'Calculus I' by same lecturer.

The secret I think to studying maths is you learn by doing. It is hard to learn maths just by reading about it. Also, always be in the process of revising earlier concepts as you learn harder and harder maths. This may be helped by taking good notes.

I also recommend that you are aware of other forms of study skills like visual mnemonics, mind-maps, cornell notetaking etc. as some of these methods may be useful and they tend to rely less on rote learning.

Finally, I have recommended on my previous posts a book called 'Moonwalking with Einstein' by Josh Foer which gives I think an interesting account of memory and memory skills which rely less on rote learning. I mention this because rote learning doesn't always necessarily lead to good comprehension and since you have a background in Psychology then there is a chance that you may find the subject interesting.

Hope this helps...

Last edited by Adduce; 07-03-14 at 06:50 AM..
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Old 07-03-14, 09:30 PM
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Re: Fastest route to Maths & Science Catchup

Hi everyone,

Thanks so much for taking the time to respond!

Quote:
Originally Posted by FreePrometheus View Post
Can you please tell me what kind of mathematics you need?
Hey that's my question ! I suppose the answer is, that I need the maths that will enable me to do the science I need to do. It's the science I need, not the maths per se, but my understanding is that you need maths to do science .. so the question is really, which science do I need (and what maths pre-reqs do I need for that)?

Quote:
Originally Posted by Abi View Post
You need Algebra and Trigonometry at High School Level, because you will use these in Calculus and Statistics later on.
Thanks Abi. My maths has not travelled in a straight line to date. In 4 years of psych study I have had to take 4 years of stats and psychometrics and I got through it all by recording the lectures, grounding away nights and weekends at the uni maths learning centre plus got a tutor. So I can "do" stats to a fairly high level .. but never really understood what was going on underneath it all.

I also had to do a fair bit of economics, simple accounting in my business degree, plus simple algebra in computer programming and I worked as a book-keeper for years so I'm numerate (but only with calculator or spreadsheet) .. just missing lots of the core knowledge I believe I will need for science.

So calculus I think we need for chemistry? Is that right? I have zero. But luckily I at least recognise those words "univariate" and "multivariate" from stats so hopefully I will recognise something!

What about differential equations? Which science are they used in?

Quote:
Originally Posted by Adduce View Post
If you get through this then there is also a lecture series 'Calculus I' by same lecturer. The secret I think to studying maths is you learn by doing. It is hard to learn maths just by reading about it. Also, always be in the process of revising earlier concepts as you learn harder and harder maths. This may be helped by taking good notes.
Thanks adduce - this looks like a great free resource! Totally agree in the "just doing it" with maths, and the online maths program I've been working with so far is all about just doing it. Just doing it 50,000 times over is how I got myself through those years of stats.

Quote:
Originally Posted by Adduce View Post
I also recommend that you are aware of other forms of study skills like visual mnemonics, mind-maps, cornell notetaking etc. as some of these methods may be useful and they tend to rely less on rote learning.
So when I say "rote learning" that included using tons of verbal mnemmonics and also would cover the walls of my flat with butchers paper and big colourful drawings and stickers and whatever as visual learning aids. But then I would rote learn all of those over and over again. Maybe it's just different definitions?

Quote:
Originally Posted by Adduce View Post
Finally, I have recommended on my previous posts a book called 'Moonwalking with Einstein' by Josh Foer which gives I think an interesting account of memory and memory skills which rely less on rote learning. I mention this because rote learning doesn't always necessarily lead to good comprehension and since you have a background in Psychology then there is a chance that you may find the subject interesting.
I couldn't agree more about rote learning not being an ideal way to go and no help for comprehension. The material I conceputally understood, but just found difficult to memorise, I found the rote learning helpful. With the stats, psychometrics and most of the psych philosophy, which I never really understood, rote learning was my only option. I read and read and read until my eyes bled. I would try and summarise stuff over and over and over again but it just wouldn't stick. If I did the calculations over and over and over again, eventually they would stick. Well, they would stick long enough to get me through the exam, but not much longer. I still don't know why that is .. I'm pretty sure it's do with very flakey working memory because stats lectures always worked exactly the same way in terms of my comprehension i.e., I'd understand the first 5 or 10 mins and then when the lecturer moved onto the 2nd or 3rd step, I would just get completely lost because I couldn't remember the first point. Every single time . Same reason I can't watch complicated movies - can't remember the first bits which help explain the later bits. I thought this was pretty common problem in ADHD but we've got a ton of super smart scientists and mathematicians kicking around this forum who clearly do not have this problem!

I'm curious how that whole stats learning process (and maths at school) would have unfolded had I had access to ADHD meds at the time. I use them now and haven't found that the primary school level online maths I'm doing particularly easy. For some reason it just doesn't gel for me and I don't understand why - I have a very high IQ, but just some sort of maths blindness. My absolute hope is that once I go back and get all the mathematical basics that suddenly my eyes will open and it will all become clear. So many times people would try patiently to explain but it just would not sink in and I would keep getting lost. If anyone has any advice on this I would love to hear it because in some ways it makes me very sad that I just don't seem to be able to grasp numbers at the deepest level. I often hear people talking about the "beauty" and "elegance" of mathematical form but it just seems completely elusive (and horrific) to me at this point in time. I'm currently taking motivation from Shinzen Young having a fairly similar story with maths and I'm secretly convinced he's ADHD, in the most awe inspiring way!

Anyway, given at this stage it's the science I need to learn, it doesn't even really matter if I can only rote learn the maths, as long as it enables me to do the sciences. Question is which sciences?

So one example of a present learning challenge, is wanting to be able to understand papers coming out on how meditation can lead to changes in gene expression and regulation of inflammatory responses.

What do I need to really understand these topics? I can rote learn the points and understand it loosely but I don't deeply comprehend. Which of the sciences do I need to understand what's going on beneath this?

Presumably I need to have biology (which?) and chemistry (which?) .. physics? And which maths to learn the bio and chemistry (and possibly physics)? I'm sure I read somewhere that the higher sciences are built on some sort of vertical model like the old computing OSI model? But I also know you wouldn't need all? Again I'm really time poor so need to find the most efficient way through this.

Sorry this is such a ramble but it's hard to explain what you don't know, when you don't really know what you don't know ..

Ruby

Last edited by ruby.149.42; 07-03-14 at 09:41 PM.. Reason: Typos
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Old 07-03-14, 10:07 PM
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Re: Fastest route to Maths & Science Catchup

Hi Ruby - have you looked at Khan Academy online? Free and very good...

https://www.khanacademy.org/
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Old 07-04-14, 01:14 AM
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Re: Fastest route to Maths & Science Catchup

Life Sciences aren't my forte but I have seen Differential Equations arise in a Biology text I was reading.

I suggest you familiarise yourself with the basics of this topic, so when you encounter them later they will be familiar. You can then study more advanced techniques as needed.

TygerSan and Namazu will know exactly which areas of Mathematics are most important for you.

As far as Physics is concerned you want to take some sort of succint course in "Physics for Life Sciences" or some such. You don't need to go into the subject in depth.

You'll need a fair amount of Chemistry and the Cellular (as opposed to Environmental) aspects of Biology and Biochemistry. There's no real shortcuts there.
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Old 07-04-14, 05:11 AM
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Re: Fastest route to Maths & Science Catchup

Thanks for replying to my post

Regarding which maths you need, a good grounding in basic maths is probably what I would recommend for all future scientific courses.
Although it sounds obvious, a good working knowledge of algebra, geometry and trigonometry are the most important for all later work that involves calculus, which is the bedrock of science courses (although there are a lot of non-calculus based science courses).

This basic maths will be the best springboard for any science course. It is obvious that there is a large difference between the level of maths you will need for different courses but what most higher level university courses build on are earlier concepts which hopefully would have been mastered earlier.

Regarding the science courses, again depends which areas of science and which level. Again, say if you took a science course that referred to differential equations, these would require some past knowledge of calculus, and if you don't have any then although conceptually you may still be able to get something from the course, the actual work given to you will take much longer because the pre requisite work had not been mastered.

Also, can see what you mean by rote learning. The reason why I mentioned alternative methods of study is that the amount of repetition you said it takes you to master the processes of maths and science may be taking up time spent on conceptual understanding.

The problems you mentioned on learning in university sound very similar to mine. You obviously have tenacity which is something that has worked very well for you so well done.

Okay. Regarding the book I recommended here is a video and a paper by an educational psychologist and I hope may be of some relevance regarding working memory/study skills.

http://www.google.co.uk/url?sa=t&rct...70138588,d.ZGU



Also, there are some good revision/study guides/workbooks designed for high school students up to university age in most subjects. Although they are written for a young audience, they are generally written to get students through the exams so are very good for cutting out all the unnecessary info. I liked the revision guides by CGP when I started studying again.

Hope some of this info is useful.

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Old 07-04-14, 09:03 AM
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Cool Re: Fastest route to Maths & Science Catchup

Hi there

I did exactly what you're talking about, 12 months ago. I had to get up to speed in a real hurry, for maths and biology. Initially I did a uni (college) course on iTunes U . You watch the videos in your own time, it's free. Dr Fern Sisser was the lecturer. Fantastic, but it took hours and hours, over weeks.

I did a prep yeear in 2013, to prepare for starting uni this year. I chose Sociology, and Intermediate Maths in the prep year. I did calc and trig and maths in high school, but 35 years later I couldn't even remember what a bloody quadratic equation was!! I was recommended two brilliant sites: Khan Academy, and Quizlet. Free, short learning modules.

Sal Khan is a education evangelist! He's world reknowned for online education. He's all over TedEx.

After my prep year in 2013, I started a uni degree this year - Biology and psych subjects. Khan Academy saved my ****. It's a really enjoyable way to learn, and there's no shame in having to repeat the lessons until you're getting 100% in the quizzes.

Quizlet is also brilliant in a completely different way.

I'm now pulling HDs. I can highly recommend these two particular sites.

All the best.
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Old 07-09-14, 10:21 PM
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Re: Fastest route to Maths & Science Catchup

Quote:
Originally Posted by Adduce View Post
Thanks for replying to my post

Regarding which maths you need, a good grounding in basic maths is probably what I would recommend for all future scientific courses.
Although it sounds obvious, a good working knowledge of algebra, geometry and trigonometry are the most important for all later work that involves calculus, which is the bedrock of science courses (although there are a lot of non-calculus based science courses).

This basic maths will be the best springboard for any science course. It is obvious that there is a large difference between the level of maths you will need for different courses but what most higher level university courses build on are earlier concepts which hopefully would have been mastered earlier.

Regarding the science courses, again depends which areas of science and which level. Again, say if you took a science course that referred to differential equations, these would require some past knowledge of calculus, and if you don't have any then although conceptually you may still be able to get something from the course, the actual work given to you will take much longer because the pre requisite work had not been mastered.


Thanks! Just finished watching the video - excellent and highly recommend. I'd seen the Memory Palace idea on a TV show once and will try it out.

Very interesting point that these metacognitive techniques were around 2,500 years ago but are not taught very much these days.
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Old 07-09-14, 10:23 PM
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Re: Fastest route to Maths & Science Catchup

Quote:
Originally Posted by MADD As A Hatte View Post
Hi there

I did exactly what you're talking about, 12 months ago. I had to get up to speed in a real hurry, for maths and biology. Initially I did a uni (college) course on iTunes U . You watch the videos in your own time, it's free. Dr Fern Sisser was the lecturer. Fantastic, but it took hours and hours, over weeks.

I did a prep yeear in 2013, to prepare for starting uni this year. I chose Sociology, and Intermediate Maths in the prep year. I did calc and trig and maths in high school, but 35 years later I couldn't even remember what a bloody quadratic equation was!! I was recommended two brilliant sites: Khan Academy, and Quizlet. Free, short learning modules.

Sal Khan is a education evangelist! He's world reknowned for online education. He's all over TedEx.

After my prep year in 2013, I started a uni degree this year - Biology and psych subjects. Khan Academy saved my ****. It's a really enjoyable way to learn, and there's no shame in having to repeat the lessons until you're getting 100% in the quizzes.

Quizlet is also brilliant in a completely different way.

I'm now pulling HDs. I can highly recommend these two particular sites.

All the best.
Sounds fantastic! Will check out Khan and Quizlet - thanks so much .
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Old 07-10-14, 03:21 AM
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Re: Fastest route to Maths & Science Catchup

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Does anyone know of any sort of info hierarchy of maths and science and how they all fit together?
Excellent question.

I lost faith in maths when I failed to agree with the mathematical axioms - you know like the existence of 0 and infinity and the way they're handled.

I think that physics helps to define a pattern which extends into science.

Note that maths is secondary to mind arises from brain
- and that brain arises through evolutionary progression which develops brain

ie

physics -> chemistry -> brain -> mind -> maths -> words (psychology)

People want maths to be be fundamental - I think that there's a progression defined by physics (eg evolution of subatomic particles) which defines an organizational principle which defines the way the mind works defines how the mind shapes mathematics.

Here's a simple example - imagine a pond - there's no way of affecting all of the pond by throwing a stone in.
Maths tries to partition parts of the pond and analyse sections without considering the whole
- there is no (in reality) way of modelling any system without modelling all systems.

So - this idea makes maths incomplete - but is maths useless ?

It's useful (engineering maths) as (I guess) approximation - but - there's something of a problem which my mind feels when it considers maths as a useful approximation ie

there is no such thing as a circle in reality

- because my mind wants maths to be a means of eliminating approximation.

-*-

Maths then - as best I can see it - as a means of creating an entirely false but consistent model reality ie we can create a virtual circle and make it roll on a computer screen ... ... and it'll behave as we define it should
- but in reality we can not develop a true circle and roll it on a friction-less surface.

-*-

So - as somebody who has started a few maths degrees and a few science degrees - I'm dissatisfied with both maths and science as approximations ie most likely eg engineering maths sufficient ... ... but no more.

Much prefer computer logic or the field of logic to others - it makes more sense - at least to me. The remarkable diversity we obtain from a single logic gate in a computer - the generation of a consistent worldview (the program) as opposed to a seemingly confusing and divergent reality (mathematical models can extend infinitely).

I'm trying to make the idea that maths consists of numbers and words.
Numbers can diverge (ie infinite numbers/models involving models).
Tying words together can lead to convergence (words weed other words out as unnecessary).

It's often said in maths that publications require no references to other's work - as if mathematics can generate research publication which isn't tied into the larger body of understanding ie divergence. Also recently heard that the current Head of Cern (Sir someone or other) mention that theoretical maths/physics were areas where it's possible to very easily find an area which one can satisfy oneself - but almost impossible to find an area which satisfies others
- once again the idea of divergence.

-*-

The point I'm trying to make is that logic (if the structure is consistent) prunes divergence.
With deliberate reference to the mind as being as structure which we're attempting to converge on a model of understanding as opposed to all individuals with divergent and non-consistent world views with all other people.

2 strands to maths then - confusing divergence vs satisfying convergence ?

-*-

So that's a whistle stop tour through how I see maths, physics, computing, language, philosophy, psychology and medicine
ie in combination.

-which isn't how they're taught

To be honest maths is my only concern - I describe it as the only subject that I'm both phenomenally interested and absolutely disinterested in.

It's interesting that certain famous medical research journals have used the idea - that if your research requires maths/statistics - then we're not interested in it.

The ability to lie through maths / statistics
- whether because nobody understands the conditions of application of your technique, or intentional subterfuge (deliberately missing out a confounding variable) or simply not generating a model through lack of knowledge which is representative.

I struggle with the merits of maths and wonder whether we should keep maths simple in the real world (engineering maths) and/or to keep it consistent in the virtual world ie to somehow prevent maths from extending itself into areas where it becomes false.
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Acquisition of quality (through learning proper) NOT money -centric.
Therefore we can not pay attention to pointless pursuits geared towards money/power acquisition.

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Old 07-10-14, 03:33 AM
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Re: Fastest route to Maths & Science Catchup

So perhaps the best way to understand maths and science is to work out what question you want answering ?

I find it's really hard learning information which I'm not interested in knowing.

In theory - maths should be the easiest subject to teach - but it turns into the hardest
- the question is - why is that ?
And is it hard or boring ?

If I look around me (a school) - people seem to like maths (school level) for its simplicity ie there's only 1 answer (not true in english/history)
- and because there's kudos in mathematical ability and a guaranteed job with mathematical capacity.

But none of that should be a concern - by that I mean - that the attraction to maths isn't as one would think.

Last maths tutor I spoke to explained that her addiction to maths resulted in marriage breakdown.

That's a really interesting idea - and may feed into the idea of warring belief systems ie divergent belief systems existing out of consistency with group - with no chance of convergence.

Once again - this line of convergent and divergent ie systems and molecular thinking comes to mind.
The goal isn't knowledge (potentially infinite) but understanding (not infinite).
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Acquisition of quality (through learning proper) NOT money -centric.
Therefore we can not pay attention to pointless pursuits geared towards money/power acquisition.

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Old 07-10-14, 05:33 AM
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Re: Fastest route to Maths & Science Catchup

Quote:
Originally Posted by ruby.149.42 View Post
Thanks! Just finished watching the video - excellent and highly recommend. I'd seen the Memory Palace idea on a TV show once and will try it out.

Very interesting point that these metacognitive techniques were around 2,500 years ago but are not taught very much these days.

Some other videos here that you may also find interesting. Hope I'm not going too far off topic!









And some revision tips for students.

http://www.telegraph.co.uk/education...orgetting.html

http://www.telegraph.co.uk/education...they-work.html

http://www.telegraph.co.uk/education...ing-facts.html

http://www.telegraph.co.uk/education...ry-palace.html
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Old 07-10-14, 11:28 AM
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Re: Fastest route to Maths & Science Catchup

I'm a bit unusual in that I never actually took a true math course in university. I got through univariate calculus in high school (college/university level class) and tested out of the math requirements for uni.

That said, if you're going into a biological science course these days, the math is going to be more intense than it has been in the past (due to the massive amounts of data mining/statistical techniques used these days).

For basic Chemistry, you'll definitely need college algebra. Balancing chemical reactions is all basic algebra (really wish that someone had told me that when I was doing it; would've simplified my approach greatly), and kinetics/concentrations/etc is *all* algebra and related concepts. If you go beyond basic chemistry, you'll definitely touch on some calculus-related topics as well.

For the stats stuff, honestly, there's sort of two schools of thought regarding stats. It's sort of like the difference between a theoretical physicist and one who actually does experiments in the real world. The theoretical ideal, and how each test is applied in practice are often quite different, and you'd be hard-pressed to find a biologist/scientist who actually understands and can tell you all the ins and outs of the stats they use on a day-to-day basis. So, if you have a global understanding of what a test does, and how it's applied (and what problems you're likely to encounter when using it), you're honestly a bit better off than if you understand the nitty-gritty mathematics but have a hard time understanding how to apply it to real-world problems.
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