I have written thousands of lines of C and C++ code to do various things from scientific research, to controlling robots and electronics, all the way to writing video games. In my opinion, C and C++ are the best languages to learn to program since most other languages are similar to, or derivative from, these.
If I were tutoring a student in programming I believe the best technique would be to just get down to writing programs and then discuss the aspects of the programs that the student finds confusing.
I have been coding in C and C++ for years. I can write programs in plenty of object oriented languages and I wrote part of the control systems for the James Clerk Maxwell telescope on the summit of Mauna Kea in Hawaii in C++.
If I were tutoring a student in programming I believe the best technique would be to just get down to writing programs and then discuss the aspects of the programs that the student finds confusing. We could discuss the philosophy of programming, the structure and interface of the language, and what aspects are needed, for example, if you wanted to invent your own computer programming language.
I have taken all of the standard differential equations courses in college while I was getting my undergrad, masters, and PhD in theoretical physics. We used Kreyszig's Advanced Engineering Mathematics for the 2nd diffeq class. I can do power series solutions, Frobenius method, laplace and fourier transforms, etc.
I can tutor discrete math, sequences and series, combinatorics, logic, set theory, etc. I took courses in discrete math during the process of getting my degrees and PhD and I have all of the textbooks and reference material need to tutor it.
I have taught the freshman electrical engineering courses at university and I have also spent several years in the power generation industry doing power system analysis.
I can tutor all of the calculational aspects of the subject including robotics, cyclotrons, synchrotrons, accelerators, electronic circuit analysis, transformers, 3-phase transmission lines, fault analysis, SPICE, PSS/E, etc.
I took linear algebra and abstract algebra as well as graduate abstract algebra in college. The text we used for linear algebra was Serge Lang's book.
I have been running Unix since 1992 and linux ever since the Halloween release of Redhat back in 1994. I have used linux for tasks from simple desktop use, to control systems, server administration, network administration, and data analysis.
If I were to tutor a first time linux user, I am fairly confident that the student would begin to use some distribution of linux as their primary operating system.
I am also open to tutoring experienced linux users in aspects of system and network administration or using linux for control systems, data analysis, or RAID arrays.
I did most of the calculations for my Master's degree in Nuclear Physics using Mathematica. Nowadays I use Maple, Form, and Octave more often but I still know how to do everything in Mathematica as well.
I have taught the freshman courses for Mechanical engineering and can tutor any of the mathematics or physics material including structural design, materials, dynamical systems, fluid dynamics, etc.
I have been running Unix since I was a graduate student at an accelerator laboratory using SUN workstations and I have used Linux exclusively on all of my computers since the Halloween edition of Redhat came out in October of 1994.