I think that Paul Wellin's recent book "Programming with Mathematica®: An Introduction" is quite good. Paul was the head of training at Wolfram Research for many years. The book is for Mathematica 9: it came out a year before version 10 came out, so the new things from version 10 are (obviously!) not discussed.

http://www.amazon.com/Programming-Mathematica-Introduction-Paul-Wellin/dp/1107009464

Nancy Blachman's book is quite good too but it is 13 years old and Mathematica had grown very considerably since then.

Hello David,

Thank you for the clarification. Your suggestion is strangely reassuring. "Search documentation for keywords". I feel less like I am somehow being dense for not simply grasping it. Good, I shall search the documentation. I guess that I am wired more towards understanding a small set of simple commands which get combined to make a program (procedural), rather than a large set of powerful commands that can almost be whole programs in their own right.

This brings interesting questions on how do we learn? Are others in this community like me? Or is it just that I have been "programmed" to be more comfortable with the procedural approach thanks to having started with Fortran, then Basic, Assembler, C, C++, C#. Are there people in this community who find Mathematica "obvious" and "natural" to use?

I wonder if anyone in this community has a book to recommend. I have "Mathematica, a practical approach", 2nd Ed, by Nancy Bachman and Colin P. Williams. I will of course be looking at the ample documentation in Mathematica, but I like having a book I can hold in my hands (I guess I'm old fashioned).

Well, thank you for listening to my musings, Henrick

Hi Henrick,

Dont worry. I got CC'd on both of your replies!

By the way, I would have given you the answer that Vitaliy gave you but I forgot about FindPeaks as it is a new function in version 10.

The Documentation Center for Mathematica is actually quite helpful. If you type "find peak" into its search bar, the second and third result that it returns are PeakDetect and FindPeaks. So searching in the documentation is one thing to often try first if you are wondering if Mathematica has a built in functionality that addresses a problem you are working on.

Best regards, David

Dear Vitaliy, Thank you very much! This is just what I needed. My problem is that I was not aware of the existence of the FindPeaks function, so of course I was trying to figure out how to do this in a functional way. And I just could not figure out how. The strange thing, at least to me, is that I can figure out how to implement the algorithm in 5 seconds if I need to get it done in C++ or in C#. I can then write it out in 30 seconds. THAT is what makes learning Mathematica so frustrating to me. Mathematica is the MOST POWERFUL programming language I know, but figuring out how to do things can be a long trek. There are so many functions available out there, one of which probably being EXACTLY the one you need, but unknown to you unless you read about all the functions and go "Oh, My God! Here is the function I need". But thank you very much. This is what I needed. I will still have to look at "valleys = {1, -1} # & /@ FindPeaks[-testList];" to see what it does. I can see that it multiplies the list by -1 in order to turn valleys into peaks. I am not sure what "{1, -1} # & /@" does to the result. But will look at it.

Something else. I also received an answer from David Reiss. Here it is: In[1]:= testList = {10, 5, 3, 6, 9, 15, 13, 12, 9, 15, 18, 20, 19, 18};

In[2]:= peakTrippleQ[{x, y, z_}] := TrueQ[x < y > z]

In[3]:= peakPositions[list_List] := Flatten[Position[peakTrippleQ /@ Partition[list, 3, 1], True] + 1]

In[4]:= valleyTrippleQ[{x, y, z_}] := TrueQ[x > y < z]

In[5]:= valleyPositions[list_List] := Flatten[Position[valleyTrippleQ /@ Partition[list, 3, 1], True] + 1]

In[6]:= peakPositions[testList]

Out[6]= {6, 12}

In[7]:= valleyPositions[testList]

Out[7]= {3, 9} I am grateful to him too. However, his answer was, at least to me, incomprehensible (and I am not blaming him). My point is how 2 knowledgeable people can come up with 2 such different answers. One incomprehensible (and not doing quite what I need) and one almost totally clear. It makes you wonder, as a novice, how am I supposed to do this efficiently? I could use the procedural approach, but I know (based on a Wolfram Alpha Video I viewed) that the preferred, and most time efficient way, is to use the functional approach.

So, I have a couple of questions for you Vitaliy. How long have you been writing code in Mathematica? Do you write in one of the other Procedural or Object-Oriented Languages like C++? How did you know about FindPeak? Did you just happen to read some book on Mathematica and saw that there is such a function? I am just curious to see how others learn this extremely powerful language, yet, in my view, difficult language to get one's mind wrapped around.

Again, Thank you very much for your answer Vitaliy, Regards, Henrick

P.S. Is there a way to CC: someone when replying? I would have liked to CC: David on this response.

Thank you very much for your answer David,
I would have to analyze your answer to understand what each part is doing. However, I must let you know that I received another answer by Vitaliy Kaurov, and it was exactly what I wanted and, I must say, simpler. Here it is: testList = {10, 5, 3, 6, 9, 15, 13, 12, 9, 15, 18, 20, 19, 18}; peaks = FindPeaks[testList]; valleys = {1, -1} # & /@ FindPeaks[-testList]; ListLinePlot[testList, Epilog -> {Red, PointSize[0.03], Point[peaks], Point[valleys]}]

The answer is also in the format I need which is the index of that peak and the peak value. But thank you very much nonetheless. Regards, Henrick