<p>Generally, astrophysics (and astronomy) is math-heavy. That should not discourage you, but rather act as a way of learning math: it is often easier to learn topics that you have a use for and are part of some personal project than just getting lectured about them. </p>

<p>Astrophysics is based on math because it is based on many forms of physics - mechanics, thermodynamics, nuclear physics, relativity theory and so on - plus chemistry. Mathematics is a common language that binds these fields together and allows you to combine them to build models to understand what is going on. Some parts just use some basic math, but in general calculus really is needed.</p>

<p>Mathematics in the more common "calculations with numbers" form also matters because it all starts with measuring things - where things are, how much they change, brightness and so on - and then we build and test our models and understanding from this. That also means that statistics is important for handling measurement noise and finding patterns in data.</p>

<p>One cannot really do astronomy and astrophysics without math. It would be just looking at things and making up explanations without actually checking if and how they hold true.</p>

CC BY-SA 4.0
2019-05-29T14:02:58.427Z
Being a fast learner is useful: start by learning the non-math parts as framing, and then as you try to understand them you have a good reason to dig into the math which will now be easier because you know what you want to learn. But some maths is quite general - like calculus - and it is better to learn it once and for all. Just keep an eye on the prize of understanding astrophysics.
Anders Sandberg
CC BY-SA 4.0
2019-05-22T08:53:56.997Z
So does that mean that I can learn it even I'm afraid a little on math but I'm fast learner, what do you think? I'm just discourage after I find out that it is math-heavy
James
CC BY-SA 4.0
2019-05-22T08:00:03.703Z
2019-05-22T08:00:03.703Z
Anders Sandberg
<p>For most parts of astronomy and astrophysics the level of mathematics required is not very high, compared to what a <em>mathematician</em> would call mathematics. (You are not going to spend much time on proving theorems, for example). So that is the first reason for telling you not to be discouraged by feeling nervous about maths. Much of the time, you only need to understand it well enough to be comfortable with using it as a tool. (It depends on the field, obviously: the shape of black hole event horizons is going to be a lot more advanced than the orbits of exoplanets).</p>

<p>The second reason not to be discouraged is that not only is most of the mathematics easier, it also comes with a built-in relevance to real life. What I mean is this. When you are studying maths <em>as maths</em>, your teacher (or your book) gives you a problem and you have to find the answer, and the answer could be anything at all. When you are using maths as a tool in astrophysics, the answer can't be "anything at all". It has to make physical sense. </p>

<p>For example, a recent paper I was reading was trying to answer the question "When did the violent neutron-star merger occur in which our heavy elements (such as gold and uranium) were created?". They measured the relative abundance, in cosmic dust grains, of certain pairs of elements which would have been the ultimate decay products of the original radioactive elements which were created in the merger. If you did such a calculation, and came up with the answer "the neutron stars merged 400 years ago", you would know the answer was nonsense. If you did it, and came up with the answer "the neutron stars merged 4 trillion years ago", you would also know the answer was nonsense. This built-in sanity check is actually reassuring, when you compare it with theoretical, "mathematical" mathematics. You know in advance what sort of answer you ought to be getting.</p>

CC BY-SA 4.0
2019-05-22T19:04:00.593Z
2019-05-22T19:04:00.593Z
Martin Kochanski
<p>A book suggestion:  <strong>The Big Bang</strong> by Joseph Silk</p>

<p>The main text is descriptive only, yet deep enough into the topic to be recommended for my third year cosmology course as an undergraduate.  The math that supports the concepts is covered in the Appendices and may be the best indication on how much you need to learn and in which areas to support your interests.</p>

<p>Math is just the language that you use to do the science.  The more math you know, the more types of analysis you can do.  Some simple math has far reaching implications, as in <a href="https://en.wikipedia.org/wiki/Hubble%27s_law" rel="nofollow noreferrer">Hubble's Law</a> where you can get an estimate on the age of the universe by taking the inverse of Hubble's parameter.  Likewise, <a href="https://en.wikipedia.org/wiki/Special_relativity" rel="nofollow noreferrer">Special Relativity</a> only requires high school algebra, but the implications are mind-blowing.</p>

CC BY-SA 4.0
2020-05-02T21:33:36.163Z
2020-05-05T08:32:06.677Z
2020-05-05T08:32:06.677Z
Boyd
<p>I want to learn astrophysics and astronomy, I'm very interested in it because there are many questions that popped up in my head, and really curious about things, but I'm afraid of a little bit on math, but I'm a fast learner, I can understand things quickly and easily especially if it is translated on my native language, I have learned basic trigonometric functions, special angles, trigonometry, algebra, quadratic equations, and some basic math but not calculus, will proceed on that later, and I have learned basic physics, until vertical dimension, but still afraid a little on math and equations, how can I counteract that fear? I mean I really want to learn astrophysics but I'm afraid of numbers,  can you give me tips? And can you suggest me some book? Or can I learn astrophysics without interacting too much with math? Btw, I'm just taking advancement because I'm really curious and interested in astrophysics, I'm still at high school, hope you can help me.</p>

CC BY-SA 4.0
2019-05-23T15:52:37.660Z
Statistics is also heavily required in many parts of Astronomy.
Wayfaring Stranger
CC BY-SA 4.0
2019-05-23T23:27:36.843Z
Have you found Phil Plait's ["Bad Astronomy"](https://www.syfy.com/tags/bad-astronomy) ? You can learn a lot and get some idea of what sorts of math is involved.
Keith McClary
CC BY-SA 4.0
2019-05-30T03:37:40.130Z
Consider asking in [academia SE](https://academia.stackexchange.com/)?
uhoh
CC BY-SA 4.0
2019-05-22T10:58:51.760Z
Just as encouragement: Learning math peroperly can come from a good teacher or from your own motivation. In high school I had terrible math teachers, but then an astronomy course that taught me many important fundamentals and basics. Once you have the motivation to self-study and you know how, you can achieve a lot without anyone else.
AtmosphericPrisonEscape
CC BY-SA 4.0
2019-05-22T14:38:33.770Z
Basic Calculus is a minimum requirement for almost anything in physics and astrophysics.  Consider trying a Schaum Outline series book (from a library ?) as a way of getting basic Calculus skills.
StephenG - Help Ukraine
CC BY-SA 4.0
2019-05-22T19:12:18.643Z
You cannot make any headway with astro*physics* without engagement with mathematics that goes well beyond high school level.
ProfRob
CC BY-SA 4.0
2020-05-01T16:25:40.167Z
A lot of calculus is pretty simple. An intro may be all you need: https://duckduckgo.com/?t=ffsb&q=simple+calculus&ia=web Don't go studying stellar atmospheres with this level of understanding. The multiple integrals will just hurt you.
Wayfaring Stranger
CC BY-SA 4.0
2020-05-01T23:37:23.683Z
It depends on the level with which you want to engage it. You can't follow it as a career or make contributions to the science without a lot of math. But if you're just curious you can learn a lot about it by reading non-mathematical works on it, even if you have to trust the author on a lot of things. I can't think of any titles at the moment, but just go to your local library, when it opens again, and start with some of theirs. If you really want to learn the math you have to dive into it, again and again.
Greg
<astrophysics><resource-request>
Can I learn astrophysics and astronomy with my basic math?
James
# Can I learn astrophysics and astronomy with my basic math?

(Asked by: username_0 on 2019-05-22)

I want to learn astrophysics and astronomy, I'm very interested in it because there are many questions that popped up in my head, and really curious about things, but I'm afraid of a little bit on math, but I'm a fast learner, I can understand things quickly and easily especially if it is translated on my native language, I have learned basic trigonometric functions, special angles, trigonometry, algebra, quadratic equations, and some basic math but not calculus, will proceed on that later, and I have learned basic physics, until vertical dimension, but still afraid a little on math and equations, how can I counteract that fear? I mean I really want to learn astrophysics but I'm afraid of numbers, can you give me tips? And can you suggest me some book? Or can I learn astrophysics without interacting too much with math? Btw, I'm just taking advancement because I'm really curious and interested in astrophysics, I'm still at high school, hope you can help me.

**Tags:** astrophysics, resource-request
> **Comments:**
> **username_4**: Just as encouragement: Learning math peroperly can come from a good teacher or from your own motivation. In high school I had terrible math teachers, but then an astronomy course that taught me many important fundamentals and basics. Once you have the motivation to self-study and you know how, you can achieve a lot without anyone else.  
> **username_5**: Basic Calculus is a minimum requirement for almost anything in physics and astrophysics.  Consider trying a Schaum Outline series book (from a library ?) as a way of getting basic Calculus skills.  
> **username_6**: You cannot make any headway with astro*physics* without engagement with mathematics that goes well beyond high school level.  
> **username_1**: Statistics is also heavily required in many parts of Astronomy.  
> **username_2**: Have you found Phil Plait's ["Bad Astronomy"](https://www.syfy.com/tags/bad-astronomy) ? You can learn a lot and get some idea of what sorts of math is involved.  
> **username_3**: Consider asking in [academia SE](https://academia.stackexchange.com/)?  
> **username_1**: A lot of calculus is pretty simple. An intro may be all you need: https://duckduckgo.com/?t=ffsb&q=simple+calculus&ia=web Don't go studying stellar atmospheres with this level of understanding. The multiple integrals will just hurt you.  
> **username_7**: It depends on the level with which you want to engage it. You can't follow it as a career or make contributions to the science without a lot of math. But if you're just curious you can learn a lot about it by reading non-mathematical works on it, even if you have to trust the author on a lot of things. I can't think of any titles at the moment, but just go to your local library, when it opens again, and start with some of theirs. If you really want to learn the math you have to dive into it, again and again.  

---

## 3 answers

### Answer by username_8 on 2019-05-22. Score: 3

Generally, astrophysics (and astronomy) is math-heavy. That should not discourage you, but rather act as a way of learning math: it is often easier to learn topics that you have a use for and are part of some personal project than just getting lectured about them.

Astrophysics is based on math because it is based on many forms of physics - mechanics, thermodynamics, nuclear physics, relativity theory and so on - plus chemistry. Mathematics is a common language that binds these fields together and allows you to combine them to build models to understand what is going on. Some parts just use some basic math, but in general calculus really is needed.

Mathematics in the more common "calculations with numbers" form also matters because it all starts with measuring things - where things are, how much they change, brightness and so on - and then we build and test our models and understanding from this. That also means that statistics is important for handling measurement noise and finding patterns in data.

One cannot really do astronomy and astrophysics without math. It would be just looking at things and making up explanations without actually checking if and how they hold true.

> **Comments:**
> **username_0**: So does that mean that I can learn it even I'm afraid a little on math but I'm fast learner, what do you think? I'm just discourage after I find out that it is math-heavy  
> **username_8**: Being a fast learner is useful: start by learning the non-math parts as framing, and then as you try to understand them you have a good reason to dig into the math which will now be easier because you know what you want to learn. But some maths is quite general - like calculus - and it is better to learn it once and for all. Just keep an eye on the prize of understanding astrophysics.  

---

### Answer by username_9 on 2019-05-22. Score: 3

For most parts of astronomy and astrophysics the level of mathematics required is not very high, compared to what a *mathematician* would call mathematics. (You are not going to spend much time on proving theorems, for example). So that is the first reason for telling you not to be discouraged by feeling nervous about maths. Much of the time, you only need to understand it well enough to be comfortable with using it as a tool. (It depends on the field, obviously: the shape of black hole event horizons is going to be a lot more advanced than the orbits of exoplanets).

The second reason not to be discouraged is that not only is most of the mathematics easier, it also comes with a built-in relevance to real life. What I mean is this. When you are studying maths *as maths*, your teacher (or your book) gives you a problem and you have to find the answer, and the answer could be anything at all. When you are using maths as a tool in astrophysics, the answer can't be "anything at all". It has to make physical sense.

For example, a recent paper I was reading was trying to answer the question "When did the violent neutron-star merger occur in which our heavy elements (such as gold and uranium) were created?". They measured the relative abundance, in cosmic dust grains, of certain pairs of elements which would have been the ultimate decay products of the original radioactive elements which were created in the merger. If you did such a calculation, and came up with the answer "the neutron stars merged 400 years ago", you would know the answer was nonsense. If you did it, and came up with the answer "the neutron stars merged 4 trillion years ago", you would also know the answer was nonsense. This built-in sanity check is actually reassuring, when you compare it with theoretical, "mathematical" mathematics. You know in advance what sort of answer you ought to be getting.


---

### Answer by username_10 on 2020-05-02. Score: 2

A book suggestion: **The Big Bang** by Joseph Silk

The main text is descriptive only, yet deep enough into the topic to be recommended for my third year cosmology course as an undergraduate. The math that supports the concepts is covered in the Appendices and may be the best indication on how much you need to learn and in which areas to support your interests.

Math is just the language that you use to do the science. The more math you know, the more types of analysis you can do. Some simple math has far reaching implications, as in [Hubble's Law](https://en.wikipedia.org/wiki/Hubble%27s_law) where you can get an estimate on the age of the universe by taking the inverse of Hubble's parameter. Likewise, [Special Relativity](https://en.wikipedia.org/wiki/Special_relativity) only requires high school algebra, but the implications are mind-blowing.


---

