text:
What do US universities mean when they mention anything above the "Calculus" course?
I am applying for a PhD in pure maths. Now a lot of places that I am applying to are asking for detailed lists of courses and books that I have followed for anything more advanced than calculus.
Now I am not quite sure what they mean here, because in our institute the course that was named calculus was an introduction to differential forms and theorems regarding those. And from there it went on to give us an introduction to manifolds. (This was our third semester undergrad; prior to this we had taken linear algebra, analysis 1, multivariable analysis, topology, and group theory.) I am from India.
Now if this is considered to be a basic calculus course then I am not quite sure how to judge exactly what courses are supposed to be more advanced than this.
Since some folks have asked regarding the syllabus:

Axioms of the real number system without construction, applications of the least-upper-bound- property, Archimedean principle, existence of nth roots of positive real numbers, ax for a > 0 and x > 0.
Convergence of sequences, monotonic sequences, subsequences, Heine-Borel theorem, lim sup and lim inf Cauchy sequences, completeness of R. Infinite series, absolute convergence, comparison test, root test, ratio test, conditional convergence, complex numbers, power series, radius of convergence of power series.
Continuous functions on intervals of R, intermediate value theorem, boundedness of continuous functions on closed and bounded intervals.
Differentiation, mean value theorem, Taylor's theorem, application of Taylor's theorem to maxima and minima, L'Hôpital rules to calculate limits.
Construction of ez using power series, proof of the periodicity of sin and cos.
Riemann Integration: Riemann integrals, Riemann integrablity of continuous functions, fundamental theorem of calculus.

This is the analysis 1 syllabus. I suppose this is going to be equivalent to calculus.

I don't understand your question. Group theory is part of your Calculus class? Or you took Group theory after Calculus?

group theory was a course that I took before taking calculus. I am sorry if that wasn't clear enough.

Did you take multivariable analysis before Calculus? When did you learn Mean value Theorem? Fundamental Theorem of Calculus?

yes of course. I mean it's all but impossible to even define a smooth manifold otherwise.. and to fundamental theorem of calculus was done in first sem. and mvt for multivariable was done in 2nd sem

For U.S. universities a reference to "calculus" means an introductory 3 semester sequence (sometimes done in 2 semesters, sometimes done in 4 semesters) covering the topics listed here. See also the descriptions of Math 115 (1st semester), Math 116 (2nd semester), Math 215 (3rd semester) here. The topics you mentioned are well beyond this.

@DaveLRenfro: so Integration and Derivation are not taught in high school? Or just not with rigourous proofs?

not taught in high school --- It is often the case that students (at least those intending to major in a math, engineering, or physical sciences area) will have studied these in high school (usually it's just the 1st semester calculus material), but they still have to prove competence in some way (varies with the college/university) to obtain credit or to obtain permission to take the next higher level course (these are two different things, the former requiring a higher "standard of proof" of the student's competence).

Incidentally, "rigorous proofs" are usually not done in a typical university calculus sequence. For example, epsilon-delta (or sequence-based) proofs are usually not done, although some instructors will include simple ones and textbooks usually include them somewhere (and if offered, a "honors level" sequence has them). On the other hand, the courses cover algebraic limit calculations of the derivative of simple polynomials and simple rational functions (e.g. x^(-2) and (2x - 1)/(3x + 2)) and probably sqrt(x) before the usual power rule, product rule, etc. short cuts are introduced.

@DaveLRenfro: I see, thank you!  (I wasn't aware that epsilon-delta proofs are not done in the first university courses.) Thanks!

@user111388: I wasn't aware that epsilon-delta proofs are not done in the first university courses --- FYI, because the difficulty level is so great from high school to college (in the U.S., excepting of course some especially strong high schools), the 1st semester calculus can be a big jump for students, and even though the rigor tends to increase throughout the calculus sequence, that first step from HS math is often the largest. I usually didn't do epsilon-delta 1st semester, I'd do epsilon-N sequence proofs the 2nd, and I'd do epsilon-delta (disks/balls in the plane/space) the 3rd.

@PabloBhowmik You should be able to find information about these universities' undergraduate curricula from their departments' websites: course descriptions, a list of required courses for undergraduate majors, and in some cases syllabi.

@Pablo Bhowmik:  At least in my experience, most of the 1st year undergrad math courses (and many later ones) are aimed more at science & engineering rather than pure math, so "rigorous proofs", or indeed, any proofs at all, are a distant second to practical application.  I think it would require a very large university to have a special track devoted to proofs &c.

@jamesqf I think this depends somewhat on the degree of specialization in your university system. In some countries, such as in the US, education at the university level is relatively unspecialized and programs usually do not start with specialized topics such as proof-based math. In other countries (such as in the Netherlands or Germany), you decide to do math the moment you enter the university level, and it is common to have an introduction to proofs in the first seminar, with most courses following being proof-based.

"a special track devoted to proofs" is simply known as a mathematics program in those universities, and in my experience most "good" universities have such a program (in the Netherlands, I believe all accredited universities offer such a program. The terminology "good" is awkward here, but unfortunately many countries do not make a formal distinction between post-high school education that gives me an obvious term. Maybe "research-based" would be better), they don't have to be large or are particularly rare.

@Discrete lizard: Perhaps it's the time period, too.  My BS degree is actually in Math (and Physics), because back then they dumped all the computer science courses into the math department.  (Because CS didn't exist as a degree program.)  So I'm perhaps biased by having been in a "math" department in which future programmers outnumbered aspiring mathematicians by maybe a factor of 5.

Note that the syllabus listed here is for "Analysis 1" not "Calculus", the "Calculus" course covered Spivak's "Calculus on Manifolds" as OP confirms in comments below.

This probably means anything beyond the semi-standarized three introductory Calculus courses.
Examples include:

Differential Equations
Linear Algebra
Discrete Mathematics
Probability
Statistics
Ring Theory

Or basically topics that might consider Calculus as a prerequisite to performing well in the class.
Classes that build a mathematical foundation to take calculus won't apply, like:

Algebra
College Algebra
Pre-Algebra
Any math topic "for some other non-math major" (Statistics for Business majors)

To clarify I've attached the University of Houston's Math department class offerings.   Note that Calculus I, II, and III are 1000 (Freshman) and 2000 (Sophmore) level courses.  I would assume any 3000 or 4000 level course would satisfy the requirement, and possibly some of the 2000 level courses.
This should help clarify some of the comments about "Algebra" courses.  Higher level Algebras that would be post-Calculus include:

Elements of Algebra and Number Theory
Abstract Algebra

I hope this provides a little more clarity.

ok so basically. this pretty much means every math courses that I have ever taken. Thanks..

@PabloBhowmik Glad to help.  Sounds like you have your prerequisite covered.

There is the unfortunate aspect of mathematics that the "Algebra" that studies group theory would count as more advanced than calculus, while the "Algebra" that culminates in the quadratic formula would be less advanced than calculus.

What do you mean by "College Algebra"?

@Acccumulation "College Algebra" is a remedial course for those who cannot place into the introductory Calculus courses.  It is sometimes termed "College Algebra" instead of just "Algebra" in undergraduate class listings.  I'm not 100% sure why they chose this terminology; but, in the USA it may have to do with the variance of learning in High School Algebra offerings.  It covers algebra including basic trigonometry, basic matrices, etc.

Regarding the name "College Algebra", this has been used for a long time in the U.S. and I have many older texts on my bookshelves (acquired since the early 1970s) with that name. Some of the more widely used older texts with that name are Henry B. Fine's book (1904; quite advanced by today's standards; archive.org copy), Rietz and Crathorne's book (1909, 1919, 1929, 1939, 1951, 1958; (continued)

1919 archive.org copy), William L. Hart’s book (1926, 1938, 1947, 1953), Palmer and Miser's book (1928, 1937), Raymond W. Brink’s book (1933, 1951), Moses Richardson's book (1947, 1958, 1966, 1973; 1958 archive.org copy).

Incidentally, "remedial" is a technical term at many colleges/universities, and College Algebra rarely qualifies, as one can obtain college credit at most places. Remedial usually ends with Intermediate Algebra (typical content: properties of numbers; fundamental operations with algebraic expressions; polynomials; systems of equations; ratio and proportion; factoring; functions; graphs; solutions of linear inequalities; and linear and quadratic equations). Also, College Algebra was a lot more standard as a first math course before roughly the 1950s, and often calculus started in 2nd year.

Actually, "remedial" is hardly ever used anymore, at least not officially. The current official PC term is "developmental". The college algebra texts I cited earlier were for a different era and were not designed for remedial purposes.

@DaveLRenfro It's true that you won't find the word "remedial" in the course offerings; and, that Algebra will often give one college credit.  However, it is important to clarify what kind of college credit Algebra gives.  It's typically the kind of credit that rarely satisfies a degree requirement, unless it is counted as a "Math elective"  My Computer Science degree (which is honestly an applied branch of discrete Mathematics, in my opinion) would only permit Algebra to be applied against the degree program as a "free elective", with math electives having to be 3000 (Junior) level or higher

These things vary a lot. I've taught at a university that didn't offer college algebra (lowest was a precalculus/trig course) and I've taught at a university where probably nearly half the students didn't place into college algebra. And credit varies greatly by both university and major. For instance, my wife was looking into getting a BSN (Bachelor of Science in Nursing) degree at one place I taught at (she's an RN, and also has a Bachelor's in English), and when they looked at her transcript they said she would have to take college algebra because it wasn't on (continued)

her transcript and college algebra was required there. She pointed out that she had taken Calculus 1, Calculus 2, and linear algebra, but this didn't matter. In particular, they said linear algebra wasn't college algebra, and they require college algebra. She wound up taking some courses in English literature (she was thinking also of getting an MFA degree -- Masters of Fine Arts) and gave up the BSN then. However, a few years ago she did get her BSN, this time at a much more highly ranked university, and guess what --- at this university they said her background took care of college algebra!

I think your question is:  What does calculus mean?
Calculus would usually include learning to compute derivatives and integrals.
If you are learning to prove the theorems used to compute derivatives and integrals, that would be more advanced than calculus.

linear algebra analysis 1, multivariable analysis, topology, group theory

All of those would usually be considered more advanced than calculus.

Just out of interest: could you say which courses are not more advanced than calculus? Are there any?

Nothing is completely standardized in the US, but precalculus, "college algebra", and introductory statistics might be common examples.

Ok sry about dragging this further but what exactly is precalculus college algebra ?
( I tried googling it but the varied response from different places seems sorta overwhelming )

@Pablo: Precalculus generally covers the behavior of certain common functions (polynomials and trigonometric functions) for students as a preparation before their first exposure to calculus. College algebra is basic equation manipulation ("solve for x"). If you're majoring in mathematics you probably took them before college.

As far as the US is concerned, "Calculus" is the first introduction to the material. It typically is light on proofs and often geared to the Engineering Curriculum. In Germany (where I grew up) this material was partially high school, partially (in College) classes called ``Higher Mathematics for Engineers''.
To get a more detailed idea,
http://www.cds.caltech.edu/~marsden/volume/Calculus/
are (by now somewhat old, but the material has not changed) Calculus textbooks that would be at the upper (more ambitious) level -- many books are weaker.

In the USA, we had already covered most of the Calculus I (limits and derivatives, and very basic integration (fitting quadrilaterals under curves) topics in High School; however, I was very aware that others had not taken these courses as they were electives.  The USA High School elective system permits various classes to be optionally taken, and "higher" math classes compete with music, drama, speech, art, auto mechanics, higher level science, foreign languages, computer classes, wood shop, school sponsored early work entry, and any other non-core class.

In light of various clarifications, here's the bottom line for your current situation: You should definitely include this course on a list of courses you have taken "more advanced than calculus" for the purposes of US universities.  And you should call it "Analysis" (or maybe "Real Analysis"), not "Calculus".
More generally, the other answers and Dave L Renfro's comments have explained well the difference in how those two labels are used in naming undergraduate university courses in the US.  It's not always widely appreciated (either in US academia or elsewhere) that the distinction between those words in US course titles may differ from how they are used either to refer to fields of mathematics (independently of naming classes) or to name courses in other countries.

Thanks for your input but given in my transcript it's mentioned as calculus also given other than this there are 3 other courses which are called analysis (I ,II, III)  I don't suppose I should be liberal about this abrupt name changes.
Also given the calculus course is sorta computational ( computing tangent spaces , working with differential form etc ) I suppose there is valid reason why folks in our department chose to call it calculus.

Some schools literally call their real analysis undergrad course "advanced calculus". It's essentially calc one but with rigorous proofs for everything.

@eps That's a good point.  Although some other schools use "advanced calculus" to mean a somewhat more advanced real analysis course, which focuses on rigorous multivariable calculus and the beginnings of manifold theory.  There's really no way to know exactly what's in a given course just from the title.  (But I strongly doubt that it's really important for the OP to provide that much detail in this context anyway.)

This answer is incorrect, because OP has been extremely confusing in sometimes talking about their "Analysis 1" class and sometimes their "Calculus" class (because in both cases they want to know if it's US "calculus").  Neither is US Calculus, but the course called "Calculus" was not a Real Analysis course (that was "Analysis 1") but rather "Calculus on Manifolds."

@NoahSnyder: I gave the answer that appeared to me to be correct at the time I wrote it, based on what had been written in the post and various comments up to that point.  Since then the situation has gotten murkier (at least from my point of view), including the very basic point of just how many different courses are being discussed.

But in the hope of giving some more clarity for the sake of anyone reading this thread in the future, let's point out explicitly (as you said in your answer) that courses named "Advanced Calculus" and "Calculus on Manifolds" do not count as "calculus" classes.  They are definitely "above calculus".

@MarkMeckes: No worries, it's not your fault, the wording of the question is incredibly confusing!

You can get an idea of what constitutes "Calculus" by looking at the Calculus AP test.
You can get an idea of "pre-calculus" with the UC admission requirements:

Three years of college-preparatory mathematics that include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry. A geometry course or an integrated math course with a sufficient amount of geometry content must be completed. Approved integrated math courses may be used to fulfill part or all of this requirement, as may math courses taken in the seventh and eighth grades if the high school accepts them as equivalent to its own courses; also acceptable are courses that address the previously mentioned content areas and include or integrate probability, statistics or trigonometry. Courses intended for 11th and/or 12th grade levels may satisfy the required third year or recommended fourth year of the subject requirement if approved as an advanced math course.

There are a few courses that are "parallel" to Calculus , neither pre-requisites of Calculus, nor having Calculus as a pre-requisite. In the case of Statistics, the subject does rely on Calculus, but there are basic courses that don't require students to actually do Statistics, so they may be considered "before Calculus". Most other parallel courses would probably be considered "after": Abstract Algebra, Number Theory, Complex Algebra, Linear Algebra, Logic, Set Theory, Graph Theory, Topology. My interpretation is that if it's not taught in American high schools, it should be included.
If in doubt, it's probably better to put something in that you shouldn't than to leave something else that you should have. They probably put this qualification in to save you time, and assure you that you don't need to put in every single math course you've ever taken.

I might call the class you called “Calculus” instead “Calculus on Manifolds,” which is the name of a famous text by Spivak covering that material.  Even though it has “calculus” in the title everyone would consider it “more advanced than calculus.”

Funnily enough that's the book that we followed. :)

Great!  People know that book and you’re listing the textbook so it’ll be easy for them to understand.  Maybe the honest but clear thing is to write the title as “Calculus [on Manifolds].”  Square brackets means words you’ve added for clarity that aren’t in the original.

Other courses besides those indicated in earlier answers could be:
Numerical Analysis, Complex Variables, Mathematical Statistics, and Theory of Functions.


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What should I ask a potential PhD advisor in an informal interview?
I emailed a professor at a school I am applying to, outlining my research interests, two specific projects proposals, and how they align with his research. I let him know that I am applying and I'd be interested in working together and chatting if he's taking students. He said he is taking students and asked if I'd like to set up some time to talk.
What do I talk about?
Here are the main topics regarding his research I can think of:

How did you come to your line of research?
What topics do you feel are under-explored in our sub-area?
What projects are you most actively working on now?

Should I also ask for feedback on my proposals, or would that sound stupid?
To clarify, I closed my email with something like: If you are looking for graduate students and feel our interests align, I'd like to discuss opportunities for working together.

These questions are more likely to  be asked by the advisor to a potential candidate but I like "What topics do you feel are under-explored in our sub-area?" also as a question to the advisor. (Be sure to have a good answer ready since you will probably will be asked yourself.)
I will give some advice which is not quite an answer to the question. Find out who the professors former students were. Look at their publication record. Do they write whatever is considered a sufficient amount of papers in your field (with the professor)? Do they stay in academia?

"How many students have you supervised and where are they now?"

Actually, your questions sounds like you are trying to hire him for a position, whereas he would be the one taking on an obligation to you and your future. I would probably have a chuckle if a student asked me those in a first interview. The first question would be good over coffee after we'd worked together for a while. For the last question you might first find a couple of his recent papers rather than ask.
But the more important questions are things like

Can you help me find a topic that interests both of us? Follow up on this question if some suggestions are made.

How independent do I need to be (do you expect me to be) and are you available to help if needed?

How successful have other students of yours have been in completion and in their careers?

Is there a seminar in which you and grad students share ideas?

If you already have a topic that you want to work on then:

Do you think ABC is a fruitful line of enquiry and (if so) can you help me explore it?

But approach such questions cautiously. Some will take offense. Be prepared to be the answerer of questions, not the asker.

"Would you mind introducing me to one or more of your current/former students?  I'd like to ask them some questions as well."

You say "If you have a topic that you want to work on". I thought that outside of a few select fields such as Mathematics, PhD students are always supposed to come with a topic in hand. Is this not true?

In the US science context, it's much more common for the advisor to propose the topic (often times as part of funded grant proposal) and then find a student to take on the topic.  It's relatively rare for an incoming PhD student to propose their own dissertation topic.

Contra Buffy, I think the questions of in the original post are quite good, and in fact for precisely the reason that when choosing your advisor you are in effect hiring them for a job: the job of guiding you for the next 5 or so years.

One of the questions I asked potential PhD advisors that always provided a lot of insight was "What distinguishes a great grad student from a good one?" It frames things positively and professors will usually tell you exactly what they expect from you.

I'm surprised no one suggested this yet:

Read some of the professor's recent papers and ask specific questions about the papers. This can pique their interest in working with you far more than a lot of the other things you're considering to ask.
Furthermore, if you have ideas on how to extend the work in their recent papers, you could bring that up and ask about the feasibility of working on such extensions of their recent work.
If you are very keen you might even read some of the literature surrounding the professor's recent work, and ask questions about that. For example if the professor's most recent work compares their own novel method to some benchmark dataset, and you find that others are also comparing to the same benchmark dataset, you might wonder about the differences between the two (possibly competing!) methods that are capable of doing something similar.

PhD supervisors often love it when their student (or potential student) is capable of reading and understanding papers on their own, then drawing their own connections foreseeing their own interesting research avenues.

From the professor's perspective I've got to say that this smells a bit of sucking up. I could be impressed if the candidate came up with something really good connecting to some of my papers, but chances are if the student has their own independent ideas, thought through for quite some time, they will be better than what they could come up with taking a few hours to read my papers. If the student suggests something related to my work just for the sake of it and it isn't a particularly good idea, I will like this less than a fine independent proposal.

A student having read and understood my papers, and being able to discuss them, is the single best thing they can do to improve their chances of working with me. If you want to called them "sucking up" for doing that, then so be it.

Fair enough if they do it well. But chances are they need to invest proper time for coming up with something good. It may be hard. It's not an easy recipe for making a good impression. (I have seen one who tried, and really didn't do it well, that's where I'm coming from.)

I agree that it requires serious time commitment. Though my PhD application (to Oxford) was over a decade ago, arXiv still existed and I'd not only demonstrated that I'd read and understood my potential supervisors' recent papers, but also found typos and a broken citations in a pre-print that was soon to be published, and they appreciated me pointing these out in time for the final publication. I was given an offer, along with the Clarendon scholarship, which goes to the top applicant in each department at Oxford. It wasn't just because of the interview, but the interview did go well.

Yes it can go wrong if the applicant doesn't take it seriously. Such an applicant is in my opinion unlikely to be a strong candidate anyway, and at least they've spent some time reading my papers, rather than none.

I'd probably ask how he sees himself as a PhD-supervisor, what his philosophy of supervising is, and what he expects of his students.
"Should I also ask for feedback on my proposals, or would that sound stupid?" This question makes sense to me.
As the professor I wouldn't have problems with the other questions that you have already posted either. Regarding the second one, however, I'd like to clarify to what extent you mean this as a question for potential topics that I may have for you. And for addressing this, I first will have some questions for you (I agree with Buffy that it may well be that the professor does the entertainment by bombarding you with questions rather than the other way round).
PS: Buffy writes "some may take offense" regarding certain questions, and that may well be, although I wonder how big the "some" set is. Personally I have very little intuitive understanding for people who take offense facing harmless and actually reasonable questions like these.

I saw updated my question. I guess since I sort of extended the invitation, that's why I thought I'd have more of an impetus to ask questions. Though perhaps most of these 'informal' chats come from a prospective student writing something similar to me, in which case your advice holds.

From my perspective, putting myself in the role of the professor (which I am these days) this doesn't make a big difference. I'd be fine with your own questions as well as with the ones I have been suggesting, and I'd probably have more or less informative answers to all of these. Same by the way regarding the questions suggested in the other responses. There are many reasonable questions one could ask...

Interviews with potential advisors will usually include a portion (often at the end) where they ask you if you have any questions for them.  It is not necessary to use your own questioning period to try to impress a potential advisor.  By now your CV and the other aspects of the interview will have told the advisor whether you are good enough to get into the program.  The part of the meeting where you ask questions is purely for your own convenience, in case there is anything you want to know about the program you are applying to.  A PhD candidature is usually four or more years of your life, so it is not unreasonable that you might have some questions about what you will be doing during this time, and what help/resources you will have.
For that reason, it would be unusual to use this time to dig into the research interests or career evolution of the professor, and it is also not useful to spend that time on technical questions about the topic (there will be plenty of time for those later!).  More useful are questions that tell you what you can expect your life to be like if you are a PhD candidate there --- e.g.:

If I am accepted as a PhD candidate here, what would a normal week look like?

How often do you normally meet with your PhD students?  What happens if they need extra help from you?

Do you have any existing research problems that would be suitable for a PhD topic, or do you prefer students to find their own topic?  (Only if you don't already have your own topic.)

Do you know if the graduate students here socialise together much?  Do they have study groups where they get together to help each other?

When asking questions, it is best to take a light touch and don't overwhelm your potential advisor.  However, if there are any aspects of the program that you want to know about (and you can't get the information yourself elsewhere) then you should feel free to ask questions to find out what your upcoming four years will be like.

In addition to the previous comments, starting from the papers that he published, you should also consider his research group.
Generally (at least in the UK), you will have a supervisory team, with at least another advisor. It is very important to know if you can have (and trust) someone else's opinion during the project.
I would also ask what kind of support you will receive, starting from the studentship.
If the project is computer-based or if you have to do experiments, what kind of facilities you can use and how the access will be managed.
You should also have a look at the University website and have a look at what kind of support they offer for post-graduate students.

This is an addition to points mentioned in other answers.
Among the other questions do ask or try to find out about past PhD students.
What is now their future as PhD holders.
Are they in Academia?
Are they hired in a company that you would like to work?
Is it a good company? Did their PhD helped them in their career and was it required?
You are about to walk a path that others also walked before you. It makes sense to see where they are now to get some indications on where this path may lead.
Some supervisors will even list past students in their websites.
The research should be extensive and to the level of the specific lab, professor, supervisor. Even within the same school of a university there can be quite a variation.

Here are a couple more things for you to ponder:

How long has this prospective advisor been at that school?   I had a young rising star for an advisor, and he left for a lesser university after 3 years (biggest fish in the smaller pond sort of scenario).  I started new research with an older, established advisor.  It extended my grad school experience considerably.
Where does the funding come from?  If you are in engineering, for example, and your funding comes from DARPA or NASA, you might see boom/bust cycles, and end up as a teaching assistant instead of a research assistant.  If you want to be a professor, this could be good.  If not, the time spent teaching is time you're not doing your own research.
What is the typical time for this advisor's students to go from start to finish?  There is wide variation in some departments, for various reasons, and some are somewhat out of your control.

You don't have to grill him on these sorts of topics... a simple, basic question will probably get him talking, and he'll tell you more that you would have thought to ask.

I had a beyond-wonderful advisor, but I've seen some that have made things horrible for their students. I'm not talking about being demanding of hard work, but regular and seemingly arbitrary "resets" of their projects, bad technical advice that must be followed, treating them as a consumable resource etc.
Find wording that is natural to you, and ask a seemingly innocuous question whose answer may flag a basic lack of empathy, or unusual amount of self-importance.
These are easily (and often) masked by a charming disposition and skilled use of language, so a direct question like "Do you care about your students personally?" won't work.
Perhaps "If I may be so bold, would it be possible to ask what you think your students might say if asked for what they liked most and liked least about you as an advisor?" or if the style of conversation seems informal, just "What would your students say was the best and worst part about working for you? Can I ask that?"
Most honest people can probably come up with some reasonable answer, but a narcissist will soar on the first half and either struggle with or cleverly avoid the second half.

I agree with the prior answers. Since the advisor gets to choose you so he gets to ask you more questions. What you should focus on is how would he evaluate your work during phd, what he expects from you, what skills you need to learn, what kind of area should you focus on.
I also feel it is very important that you have a very transparent relationship with him. Meaning, if you plan to take breaks (like I did for the birth of my baby) be upfront about it than hiding. A transparent relationship will really help your career.

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text:
I’m being asked to research maths for my Python module. Is this right?
I’m a mature student, starting a part-time MSc. computer science degree after a decade in industry, after previously graduating with a BSc degree. I am out of touch with academia, but I am excited to get into it. I have an open mind to this all and I know it’ll be a bumpy ride.
My first module is on Python programming. The course book covers Python and a bunch of Python libraries. It’s basically just a bunch of documentation assembled in a PDF file with some Python history.
The one and only piece of graded work is a written assignment. The “task” is to take the few CSV datasets provided, matching columns in one to columns in another and matching single “x,y” pairs from another dataset to previously identified columns. The criteria for one part is the lowest mean squared error, and for the other it’s not explained quite so succinctly, but it’s a calculation. It’s not specified in any sort of terminology I can relate to, what kind of problem were solving here. The task specification is written in an imperative style and is not really explaining much of the “why”, just a prescriptive “how”.
Where I’m getting lost is, what we’re being assessed on does not seem to be much about Python. We’re to think of a research question which we should then investigate and in doing so, shoehorn this program into it as if it were our own solution to the problem which has not actually been articulated.
We must write 14 or so pages of research. The source code for the program is to be an appendix. Having seen the assessment guidelines, almost all the marks will come from the main body of text, not the source code.
In the chat with students and the course coordinator, people keep asking the same question: can they do something more related to Python? The answers is always no, because it’d be too “documentary” rather than “research”.
But the only suggested topic is always around the criteria by which one set of data are mapped to another. The coordinator makes no secret of his wanting to see us research maths for 14 pages. We have other modules covering maths and there is zero mention of maths in the module description including the learning outcomes.
Is this unusual? It strikes me as quite odd. The few people I know who have done Masters degrees are baffled to the point of annoyance at this.
NB: So far my questions to the coordinator for clarification have gone unanswered, but I only anticipate the same answers everyone else got already. I’m a student, but I’m a paying customer first, and like any sensible customer I will be sure to get my money’s worth.

Well, there are a bazillion different Python libraries. Determining which library, and which function(s) in the library to use is often the much harder problem then writing the program to do it. Documenting what your assumptions on the data and analysis are, going through the libraries to find routines, and documenting which routines actually do what you have assumed the analysis should be seems pretty reasonable, all in all. I would expect a Master's degree holder to be able to figure stuff like that out. It isn't researching 'math', it is analyzing the problem and looking for how to solve it

"Researching math" (from an applied math/statistics perspective) would be inventing Mean Squared Error as a target to minimize in an estimation problem (and explaining why that was a sensible thing to minimize, or why it's better than minimizing something else), or perhaps finding an efficient algorithm to minimize MSE for such a problem. Someone has already done that, long ago. Now that they've done that, writing code to apply their existing algorithm to some specific data is purely a programming task.

Understanding specifications and finding resources (such as mathematical techniques useful for solving the problem) are integral parts of software development.  There is more to being a programmer than coding.  It sounds to me like the course is trying to put programming into a more realistic context to give you a broader range of programming skills, rather than focussing just on "coding".

I’m a student but I’m a paying customer first, and like any sensible customer I will be sure to get my money’s worth - or else what? Be careful what you wish for - your instructor can read aloud the textbook in class and give out leetcode questions as assignments, that would satisfy the contract for "one semester of Python learning". It might even satisfy you, but it would certainly be worse teaching by any objective standard.

What department/subject area is this class in? (Alternatively, what are the pre-reqs for it?)  It sounds like a statistics class, not a language-introduction programming class.

This is exactly how you will use programming in the real world, especially as a computer scientist.  Science is carried out in the language of mathematics.  Computer science applies computation to those mathematical problems.  What, exactly, were your expectations when going into this?  Perhaps computer science is not the right field if you're looking for exposure to different aspects of software development.  If you were looking for mobile apps, games, web development, or something else then this is entirely the wrong discipline.

At masters level, a course that merely teaches elementary Python coding would lead most other students to walk up to the dean and tell him they're not getting what they're paying their tuition for.

This sounds pretty much perfectly on point as training for conducting computer science research, albeit maybe a tad artificial.

"my questions to the coordinator for clarification have gone unanswered" looks like the biggest issue here.  IMO you should be able to expect reasonable on topic questions to be answered in a timely manner by the professor/coordinator.  That's part of their job.

I think the main thing being lost by commenters here is that, the programming part of the assignment is not an issue. What I don’t get is the relevance of writing a 14 page written assignment about MSE/Linear Regression or some other aspect of the logic of the specified programming. The actual program I write is worth less than 16% of the grade. I’m being judged on an exploration of mathematical/statistical methods. Or some other methodological aspect of the prescribed program. I’ve yet to see anyone make a case for the relevance.

@pinkstudent Because when you're doing this professionally you'll spend about 16% of your time writing code - at most - and the rest of it on planning, design, architecture, algorithms, specifications, etc.  Architects don't spend a lot of time working with hammers and nails - computer scientists don't spend a lot of time writing code.  It's the core of how things are implemented, but the hard work happens before you start writing code.

I’m being asked to research maths for my Python module

No, you are not. It sounds like you're being asked to do some elementary data analysis or data science. "Researching math" is a different animal altogether...just take a look at the Annals of Mathematics to get a sense of what "researching math" looks like.

We’re to think of a research question which we should then investigate...

Sounds like a decent exercise -- here is some data, now do some work to understand/visualize the data and confirm or reject a hypothesis.

...and in doing so, shoehorn this program into it as if it were our own solution to the problem

This is a little more alarming....I hope the existing program is just a starting place which students will have to greatly modify and expand upon.

people keep asking the same question: can they do something more related to Python? The answers is always no, because it’d be too “documentary” rather than “research”.

Sounds like the instructor and the students have different visions for the course. The instructor sees this as an "introduction to data analysis using Python," while the students see this as an "introduction to Python."
It is hard to judge such matters from the outside, but I suspect the best option is somewhere in between. You are doing a science degree, not a software engineering degree, and so learning to use code to study data and solve problems, rather than just coding for its own sake, is likely appropriate. On the other hand, students with no coding background at all will need to be taught rather a lot, and so I'm a little alarmed that you only have one graded assignment for the entire semester. Coding, like algebra, is one of those things that you learn by doing, and so I would have expected you to have several hours of Python programming homework per week.

A module might be a sub part of a class that takes a whole semester

True…though I would be just as alarmed in this case; a few weeks of programming will not get them very far!

A module can be taken here to mean a class. So an independent topic of study with its own learning materials etc. We do have data science modules and statistics modules later on. I agree with your point about science vs software engineering. And I’m actually quite excited about defining my own questions, investigating, etc. I’m just a bit confused like many of the other students about the format this is taking. I will just accept it as part of the challenge. Thanks!

As far as coding background, sounds like it's a Computer Science MS, so they have that. Then even if they don't specifically know Python, a 1-week "Python for programmers" crash course would be common enough.

@pinkstudent it sounds like your degree program is more specialised than just computer science, is there a more detailed title of the dergee programme?

@AnonymousM - true, however, skimming through the Annals should clarify why OP got such a negative reaction when they referred to their data analysis exercise as "math research."

I would like to point out a software engineering degree does not (should not) teach coding for its own sake either. It should teach to use code to solve business and engineering problems. So your answer would be valid there, too.

To be fair, OP's usage of "researching math" as "doing some light self-study [googling, reading on Wikipedia] to find out what math to apply" is pretty common. When my wife says she researched what auto insurance gives us the best rate she also does not mean that she got a PhD in it. Words can mean different things to different people.

It seems as though you are been asked to use Python to solve a moderately complex problem. There is nothing wrong with that. Programming languages are written to be useful (mostly, at least) and this is just an application.
Also, you are in a masters program in CS and so the application is not that far from the mainstream of data analysis that researchers normally do. So, yes, being asked to do something hard is pretty usual at the masters level (or even undergraduate).
As for the lack of clear definitions, of things, I suspect that you are expected to find them, just as anyone would on a real project. And as you advance, the projects you will need to be able to handle won't all be simple.
I don't know how it is graded, but the structure and correctness of the implementation can/should be an important element.
This is what computer scientists do to apply knowledge to a given domain. Look on it as an opportunity.

This! At the master's level you should already know how to hold a hammer and be able to figure out on your own how to use a few other tools. It is time to learn how to do something useful with those tools.

I don’t want to say that it’s trivial but the code we must is write is almost written for us. The task is very proscriptive in terms of stating that the code must “do this then that then this then that”. Turning that into Python code does has not been hard and I don’t see other students struggling. And this is reflected in the fact that the code appears to make up a small part of the grade. The bulk of the assignment is to pick part of the unspecified problem which the code addresses, and to investigate it over 14 pages. So methods for finding bet fit between datasets etc. Anyway, thanks!

@pinkstudent That's what real data analysts do all the time. Coding is "easy", especially with all the libraries that are available these days, figuring out the problem and how to apply these techniques to it is the difficult part. You're not a beginning coder if you're in a Master's program.

Mine won't be the answer your looking for...
I'm not a professional programmer. I'm an electrical engineer. But I frequently use programming to solve problems, and the simple reality is that whether as a hobby or as a paid employee, it's my job to figure out how to use the tool to solve the problem. And that's the important point. You're not taking a class just to learn how to use the tool. You're also taking the class to learn how to apply the tool. To use a metaphor, nobody takes a class just to learn how to use a hammer. They take classes to learn how to make cabinets. And it's not unreasonable for the instructor to believe you already know how to use a clamp.
What's unfortunately hurting here is that, as a mature student, you're not taking this class hot on the heels of four years of mathematics courses, such that the instructor can reasonably assume that you have a host of pre-existing skills to immediately draw from. I can feel that pain. It's been 30 years since my last engineering class. If I went back today to get my masters, they'd rightfully expect me to remember all my Calculus courses — and I'd be buried in my old textbooks trying to remember what I once knew but haven't used in decades.
Unfortunately (and here's the part you won't like)... that's not the instructor's problem. No, I don't think it's unreasonable to expect you to do something you should have learned how to do in your undergraduate courses. But I do sympathize.
Having said that. If your co-students are asking the same questions you are, then there is a problem because that would mean the instructor is asking for skills more-or-less no one has learned. I read your post several times, but I can't come to a clear conclusion. Are the other students having the same trouble you are? Or are they asking their own questions and are only getting the same quality of answer you're receiving to your question? Maybe I should have asked about this before posting an answer... but in the long run, I doubt any argument made here will sway your instructor.

Thanks for your answer! Your empathy is valuable. In general the other student have the same questions. I think partly the written assignment document could be better written. There are three pages explaining “the task” and only seven or so words at the start which suggest that actually you need to think up your own research topic. My undergraduate contained next to no maths as it wasn’t CompSci so I was expecting lots of maths self study. Just didn’t think it’d bite me in the Python module haha! I will soldier on! Meaningful goals are never easy.

I'm inclined to agree with this answer. The OP says it's university, for a master's degree after ten years in the industry; I don't think uni is where you go to learn a programming language, it's where you learn the theories behind programming languages and what to use them for. Python is the hammer, and you don't need university to learn how to use a hammer.

I am in a different field, but your professor isn't having you research math. To you, it is researching math because you have never heard of this before.  He is making it obscure because there is an entire academic field that does this specific problem.  He has disguised it so you cannot google it.  If he had used terms that you recognize, this would be a ten minute problem, because you can google the solution.
The irony here is that the code sort of doesn't matter.  This is somewhat like a "print{Hello World!}" problem with some sophistication.
He is forcing you to work with a good requirements document that is a bad requirements document for you because you are not a subject matter expert.  He is asking you for dihydrogen monoxide instead of water.
You are not researching math, you are researching English.  He is forcing you to explore Python.  He isn't feeding you Python, he is starving you and making you hunt your own food.  While you are hunting the food, you are documenting it.
This is not an undergraduate program where you jump through a set of hoops and a degree comes out on the other side.  You are being required to prove independent mastery.  You are being required to prove that you no longer need adult supervision.
I have never taught in your field, so my only criticism might be that there should be more work and assignments.  However, there may be enough struggle in this for enough students that you would all fail if this were replicated over many assignments.  After all, it bothered you enough that you felt you needed to post about it on the internet.  It might be doing its job.

The irony is definitely not wasted on me haha! I guess you’re right, this will make it all the more rewarding once I finish it. Thanks.

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Prerequisities to become an MD-PhD?
Officially, I am studying computer science. However, what I am actually doing is computational neuroscience. More over, the research I do is mostly medical research.
I have noticed that there are programs for MD-PhDs. However, in most countries, there seems to be always some legal requirements one has to fulfill to enter such programs. These requirements are not given very clearly out in most cases.
With an M.Sc in computer science, can I apply to such programs? More trickier question is would it be wise..? I mean, I could just go to a neuroscience program. However, I would be also really interested to help people with psychological, neurological, etc. issues (work in hospital), when having the MD title is a must?

@confused Does your institution have a pre-medical school advisory team? These are usually for bachelor students who want to become MDs. They would know the specifics of what the local requirements are and how to interpret your background.

Most of the "legal requirements" associated with MD-PhD programs are financing related. In general, such programs are usually sponsored and funded by national health ministries (or their equivalents). Therefore, it is preferred (or required) only to have legally qualified citizens participate in such programs.
As for the choice of major, in general, computer science is not one of the usual entry points for MD-PhD programs, which tend to be more closely related to experimental programs and majors (e.g., chemistry, biochemistry, biology, bioengineering). That said, there is more of an emphasis nowadays on computational science in medicine, and more and more MD-PhD programs are expanding their scope to include bioinformatics and computational biology. But it is still definitely not a universal, and CS majors will be at something of a disadvantage.

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Can a discoverer give the name he wants to his finding?
Let's assume that some scientist discovers a phenomenon that has never been noticed before.
He wants to write a paper about it but he doesn't want to constantly write "effect of change of some properties blahblahblah". Can he therefore name this effect with a name of his choice? For example "Discoverer's name's effect". Or "fluffy puppy effect" (just because he likes puppies)?
The same for constants. Can one name newly discovered constant "my name constant"?
This question can be simplified to: "what are standards for naming new physical entities?"

To add a small point to Floris' good answer: in general, attempting to name something after yourself is considered a massive faux pas, and doing it would cause you to come across as unprofessional or a crank. The discoverer's name is always attached to the discovery by other people writing about it afterwards.

Here's one tactic that I have seen tried to get something named after yourself, but I don't recommend it! Give the phenomenon an awkward name in your paper, hoping that others won't want to adopt that name and that they'll end up using your name instead.

@Nathaniel thanks for the comment. I have incorporated it in my answer - with attribution, of course.

Well you can always try. Take this as an example: http://care.diabetesjournals.org/content/17/2/152.abstract (here the author, Tai, "discovered" the widely known trapezoidal rule originally probably due to Poisson circa 1820 and calls this the "Tai Model". The name has not caught on, but the paper's been cited hundreds of times according to Google Scholar)

An example from mathematics: Stefan Banach named an class of objects "spaces of type (B)" and they eventually went on to be known as Banach spaces, and I've heard it speculated that Banach chose the name in the hopes that this would happen.

@MichaelLugo: When Dickson introduced what are today called cyclic algebras, he called them "algebras of type D" and earlier in the paper he had defined algebras of type B and C. (The paper is http://www.ams.org/journals/tran/1926-028-02/S0002-9947-1926-1501341-6/S0002-9947-1926-1501341-6.pdf.) Perhaps he did that so the name "algebras of type D" would not look like a blatant attempt to name them after himself, although I suspect he hoped they would become known as Dickson algebras.

Related: http://academia.stackexchange.com/q/34555/64

Not in physics, but the creator of the unscented transform named it after the unscented deodorant on someone's desk, and the name stuck.  'Fluffy puppy effect' might be more of a stretch.

@alarge - that is a grotesque failure of the peer review system. Thanks for pointing it out. You might want to post it as an answer here?

Usually the way this works is that a researcher discovers some phenomenon and publishes it without giving a name. Then someone else comes along and writes about "Jones' discovery" and before you know it the world talks about the "Jones effect".
Giving things a name yourself is done in some fields - for example, in MRI (magnetic resonance imaging) it is conventional that people who develop a new pulse sequence will give that sequence a "catchy" name (usually some clever abbreviation, never really their own name). So you have names like CAIPIRINHA (which is really the name of a drink, but stands for "Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration").
In the end, the name that the community adopts is the name by which something will be known - so you are free to call it the "teletubby galaxy" but if everybody insists on calling it Andromeda-X42 you will be a lone voice. If you have the good fortune of discovering something new and valuable, name it wisely or be ignored.
Reiterating the point made by Nathaniel: suggesting that a particular phenomenon/constant/equation should be named after you is considered a major faux pas. Others will do it for you - when you try to jump the gun and suggest that it be named after you, you will come across as conceited. I can think of no example of a well known effect that a discoverer named for themselves. Some examples where they did not:
Newton's Laws (he called them "Axiomata sive Leges Motus")
Hooke's Law ("Explaining the power of springing bodies")
Josephson effect (for which he got the Nobel prize... not available for Newton or Hooke, or surely they would have qualified) was described by him (Physics Letters Vol 1, No 7, 1962) as "new effects":

he didn't say "we present here the Josephson Effect".

The list could go on and an. If you are the greatest, you don't need to say so - others will do it. No offense intended, Mr Ali.
If you are interested interested, there is a follow-up question on a sister site, History of Science and Math: What famous laws were named by their discoverer?

Turing machines were named a-machines (automatic machines) by Alan Turing.

“I can think of no example of a well known effect that a discoverer named for themselves.” – sounds like a question for HSM.

@Wrzlprmft thanks for the suggestion: http://hsm.stackexchange.com/q/691/543

This method is flawed as per Stigler's Law.

@RenaeLider nice link. Often, the person who gives the discovery visibility gets the credit; indeed that need not be the person who made the discovery. Think Crick and Watts, or Kamerlingh Onnes, to name just two instances off the top of my head.

@Floris And then there are really sad cases such as when somebody else is acknowledged based on no logical grounds - Jocelyn Bell's senior professor winning the Nobel for her discovery! Preposterous, I say.

Jocelyn Bell - wasn't she the one who discovered pulsars?  <starts to Google> Hewish taught me at one point... Since the nomination says "to Hewish for his decisive role in the discovery of pulsars" that is indeed a pretty sad mistake.

My guess is that if you give a catchy name to a phenomenon/algorithm, it is more likely to stick and be remembered by your colleagues. If you give it a dull name such as "$K$-machine", or "method A", it is less likely to be remembered but also more likely to be renamed after you if it's really important. (disclaimer: nothing important is named after me, so these tricks may or may not work.) :)

So basically you suggest that we should name it like "the new method/effect/blablabla" and leave the action to name it to other people?

@Ooker that seems to be the traditional way this is done. You can name it - just not after yourself - seems to be the consensus. See my earlier comment (Dec 19) for a link to further discussion.

I think you can add it into your answer for interested viewers.

@Ooker good suggestion. Done.

There are several levels in your question. A researcher can certainly come up with a name for, say, and effect observed in research. This new name should be descriptive to stand a chance to catch on because it is only when accepted by peers in the field that the name may stick. It is also possible to name effects after their first discoverers and the same applies, if any agree on it it may become used. naming something after one-self is probably a really bad idea. Trying to be funny or ambiguous equally so.
As for constants, one can certainly name a constant anything you wish but if the constant has any wide relevance there are usually organisations that will have to accept names and numbers. some of this work is done within Bureau International des Poids et measures (BIPM) that maintains the SI-system. The different Unions within the The International Council for Science (ICSU) also organise working groups (equiv.) to work on terminology and propose standards for the different fields. within different fields there are varying additional international bodies that organizes nomenclature and terminology.
So standards are usually set by standardizing organisations. There focus on terminology , constants etc. that have wide significance and where accuracy both in terms and numbers are required. On top of that the scientific community self-organizes softer terms such as those of effects or theories but the success of introducing new terminology or what have you is always depending on the peers accepting it in a longer perspective.

This answer is field-specific, as in some fields such as CS, funny and somewhat non-descriptive (e.g. acronyms that only become slightly descriptive with some convoluted explanations) names are more or less the norm.

Specific to what field? And, the question is not just about acronyms, which I agree anyone can come up with and use.

Specific to fields that are not CS or (as mentioned by Floris' answer) MRI. The question is about any names, acronyms are an example thereof, though non-acronym names certainly appear, as well.

Chemists who discover a new element of the Periodic Table have the right to name it. Marie Curie, who won a Nobel Prize in Chemistry, named her discovery "polonium" after her native Poland.
I would not be surprised to see this practice followed in other scientific fields.

Except that the modern interpretation of this is that the discoverer gets to propose a name, which IUPAC then votes on. For example, if you discovered an element and tried to name it aurium, this would probably be rejected for sounding too much like gold.

You may absolutely call your findings whatever you want. I have seen it done many many times - but some people may consider you to be an 'arrogant jerk' (shall we say) for naming things after yourself - especially if they are trivial.
I have seen trivial things being named as if it were something incredible or ground breaking, and all I think is: what a loser. Adding two numbers together that both end with the number 3, does not deserved to be called "Peter's Second Principle of Arithmetic" (this isn't actually a thing, but makes my point)
Honestly, unless you discover a new element or your finding is truly notable don't name it anything. As others have mentioned, the academic community will name it for you if they deem it notable enough.

I think there should be a distinction between possessive and non-possessive naming. If Joe Smith relates to something as his Quarkion Principle, then other people should refer to it as Joe Smith's Quarkion Observation.  Attaching the principle to himself is not arrogance, but rather the reverse; it would put it on equal parity with similar observations by other people.

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How did authors prepare figures in their publications before the advent of computers?
I am often amazed at how neat figures in old scientific publications are. How did authors prepare those plots and diagrams, when there were no computers around? Did they draw them by hand? Were there any special methods and tools involved? Did the authors prepare the figures themselves?

Re: methods and tools, http://en.m.wikipedia.org/wiki/Technical_drawing_tools is an interesting read

The existing answers about ink presumably are valid as far back as we had photo reproduction techniques. Before that, I suppose someone had to engrave a metal printing plate.

Many old images are called woodcuts. Therefore they were presumably cut out of wood and used in the press.

Ink on vellum. Depending on the work place the author may have made their figures themselves or in some cases professionals were involved who would take a sketch and draw an ink original. the techniques were basically the same as for any technical drawing using templates for creating text. A lot of techniques went into making nice figures, sometimes including adhesive rasters to create shading effects etc. A asic technique was also to produce originals is a larger size than final so that when reduced in size, small imperfections would basically dissappear in print.

The professionals, were they employed solely for scientific works?

The professionals would probably have been employed by the graphic arts department, which would have been used for whatever graphics were needed. For large businesses or universities which needed both scientific and non-scientific works, my guess is that some professionals would have specialized in scientific art.

Also, how did they reduce the size of the originals?

@adipro The printing process most likely to have been used (offset lithography), at the time, involved photographing the original and then projecting the negative onto a "plate" along with everything else that would go on that page.  The projection step allows the printer to arbitrarily adjust the size.  (Nowadays plates can be exposed directly from computer files but I am under the impression that photography is still used at least some of the time.)

@Zack, does that mean that reducing sizes was only possible after the advent of photography?

@adipro No, before photography there were pantographs and scaling grids.  But photography makes it a lot easier.

also be aware that offset lithography is dependent on photographic processes, even the new non photographic processes where plates are printed directly from a computer without the aid of any cameras is still a photographic process. (I'm not sure about the new plateless printing process.) There were also photographic processes used in the late letter press days. Prior to that they used engraving and casting.

I believe many of them did the drawing themselves with ink pen, for example. Graphs can be drawn using pins and a metal ruler: you put pins (or small nails) in a measured points of a graph, and then bend a ruler to pass through all nails. The ruler will eventually form a curve, known as a B-spline interpolant of a given set of points.

This is one of many techniques taught to draughtsman (draughtspersons?). In my father's day drafting was a basic skill for a scientist, and though I could see the CAD world coming I learned it myself, and I have never regretted it. I only use those skills every year or two, but they still have the uses.

Calvin Schmid's Handbook of Graphic Presentation has a very detailed chapter with many nice illustrations on this process.

My grandfather wrote geography books. He had some sheets of plastic with wavy lines on them, used to fill in the seas in maps. The plastic was cut to shape and glued to the paper. I assume similar things existed for other regular fills.

Gosh, I feel ancient :)
I graduated just before the Windows became popular. We had 8-bit PCs with MS-DOS and some very basic text-processing software. All the official documents (including my master’s thesis and first research papers) were typed on mechanical (or if one was lucky – on electrical) typewriter. For corrections in the typed document we used a special white fluid (applied it with a little brush over the misspelled letters and once dry retyped the correct ones on top).
All the formulas and figures had to be drawn by hand (using a special ink pen, a ruler, a compass, sometimes a special curved ruler). A piece of grid paper could be glued to the document if necessary, or if the grid was big enough to occupy a whole A4 page, we would buy a ready-made grid page from the university bookshop and insert it where it belonged.
This was the required format for conference papers and all other materials we submitted to the print shop, where they used offset lithography and some other techniques to print conference proceedings, textbooks, etc.
There wasn’t PowerPoint, so the “slides” for presentations were drawn on a big cardboard sheets (A1 or A0), which were then hang/stack/pined to the wall/blackboard. Or, if there was an overhead projector, we did the drawings on transparent plastic sheets.
There was a technician in the department, whose job was to do technical drawings, but usually she was very busy, so I did most of the drawings myself. And, yes, I had studied technical drawing as a part of my engineering degree, it was a mandatory module.

A related subject: preparation of mathematical formulas and equations. These were things that simply couldn't be done (other than very crudely) on a Linotype or similar "hot type" machine. To do it anywhere near "right", skilled typesetters needed to build up the equations by hand from tiny pieces of type and lots of pieces of spacer lead and such. Needless to say, this was very slow and very expensive and prone to error. It went "offshore" to lower wage countries, but even then was still too expensive. Crude typesetting programs existed but produced such poor results that Donald Knuth was driven to produce something that would typeset math to his standards: TeX. TeX (and LaTeX and various permutations) are still the gold standard for setting text, equations, and even some graphs and other figures (such as chemical diagrams) generated on the fly.

You will notice I said "A related subject". The typesetting of math is closely related, and leads into the automatic generation of some graphs and other figures from tabular data. Don't be so quick to condemn!


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Is it important to publish my article in a journal indexed on Thomson ISI?
If a journal is not indexed this way, is it an academically honorable one?

@dgraziotin Tourism Management. And I am from Iran but of course I am going to publish my work in English.

according to my experience publishing an article depends on which purpose you want to publish that paper and of course ISI journals have more value than other ones.

If we momentarily disregard from discussions regarding the cons of ISI and Thomson-Reuters who run the service etc. and focus on the usefulness of ISI indexed journals for ones career, the answer is yes, it is important at least to some extent. The importance is in part depending on your discipline since ISI indexing is not evenly distributed over disciplines. But generally speaking the ISI listing means the journal publishes papers that are referenced, which is an indication that it is research of some quality and importance.
This does not mean non-ISI-listed journals are not "honourable". But, when choosing a journal in which to publish, you need to make sure it is read by other in your field so that your research is seen and your ideas known by others. You should make a survey of journals that are of reference and if you find ISI-listed journals there is a reason to consider them if your papers fulfill their quality criteria because they will be  seen as prestigeous references when you are evaluated for a position etc.

I think this misses the actually important point: some bureaucracies won't count publications in non-ISI journals as "real."  If you want to get a job in a country with such a bureaucracy, that is your real issue.

@BenWebster Writing that as an answer would be valuable.

I don't think "honourable" is the correct framework to think about.  My general understanding is that most reputable journals will be ISI indexed, and so if you are considering publishing in a journal which is not, you should look hard at whether it is legitimate, and whether people in your field will respect publications in it.  You should look at the same thing for ISI-indexed journals.
 There are many journals which are ISI-indexed, and I have no reason to believe are not run legitimately, which I have never heard of, and which I would never recommend to someone I know as a place to publish (I don't want to pick on any particular one, but if you go to Web of Science and search for the name of your field, you will find plenty of them). An article in a journal I have never heard of makes a very poor impression to me on a CV, so it is worth researching more carefully what the "word of mouth" reputation of journals is in your field.