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There are three big parts of mathematics: geometry, analysis, and algebra. In this insight, I will try to give a roadmap towards learning basic abstract algebra for self-study. This includes the study of groups, rings and fields, and many other structures. Prerequisites The requirements for self-studying abstract algebra are surprisingly low. Basically, you should be…
For several years already I have been trying to help students who have been self-studying math. I did this completely free with no compensation for me. I saw this as a very enriching experience. Most of the people I helped came from physics forums. I usually contacted them and told them I might be able…
If you wish to follow this guide, then you should know how to do analysis on ##\mathbb{R}## and ##\mathbb{R}^n##. See my previous insight if you wish to know what kind of topics you need to know and for suggestions of books: https://www.physicsforums.com/insights/self-study-analysis-part-intro-analysis/ Also in many parts, you should be comfortable with linear algebra, see my…
In this insight, I will give a roadmap to learn the basics of linear algebra for students. Aside from calculus, linear algebra is one of the most applicable subjects of all of mathematics. It is used a lot in engineering, sciences, computer sciences, etc. The right way to see linear algebra is with a focus…
Geometry is one of the oldest parts of mathematics. It has been studied and advanced by the greatest minds humankind has to offer. It has been described as a subject of great beauty. How do we approach such an amazing work of art as a student? In this section, I will attempt to give you…
This is a sequel to my posts on self-studying mathematics. I have already given a very detailed road map on how to study high school mathematics and calculus. In this post and the next ones, I will try to give a very detailed road map on how to self-study analysis to reach a high level….
We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order. So in order to answer those questions, I have decided to make a list of topics a mathematician should ideally know and what prerequisites the topics have. Calculus After high school…
How to self-study mathematics? People self-study mathematics for a lot of reasons. Either out of pure interest, because they want to get ahead, or simply because they don’t want to take formal education. In this guide, I will try to provide help for those people who chose to self-study mathematics. Is it even possible…
Introduction We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order. So in order to answer those questions, I have decided to make a list of topics a mathematician should ideally know and what prerequisites the topics have. Basic stuff Of…
We asked our PF Advisors to tell us what academic advice would you tell your 18 year old self. Here are their responses… Thanks to all the PF Advisors that shared their academic advice. We have more questions for them in the near future. Stay tuned for another “Ask the Advisors”!
Introduction For the past few days, during my summer break, I have been intensively self-studying mathematics (namely number theory) for several hours each day without having prior experience in theoretical math. The struggle of learning is not unique to mathematics; during my first year of computer engineering (which I had just completed at the time…
Introduction I am convinced students learn Calculus far too late. In my view, there has never been a good reason for this. In the US, they go through this sequence of Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus, Calculus 1, and Calculus 2. But is this required? Recently I came across two books that turned…
We asked our PF Advisors to tell us their most memorable or influential textbook and why. Here are their responses… Thanks to all the PF Advisors that shared their favorite textbook. We have more questions for them in the near future. Stay tuned for another “Ask the Advisors”!
Preamble The classical mathematician practically by instinct views the continuous process as the “real” process, and the discrete process as an approximation to it. The mathematics of finance and certain topics in the modern theory of stochastic processes suggest that, in some cases at least, the opposite is true. Continuous processes are, generally speaking, the…
Abstract “Mathematics is the native language of nature.” is a phrase that is often used when it comes to explaining why mathematics is all around in natural sciences, especially in physics. What does that mean? A closer look shows us that it primarily means that we describe nature by differential equations, a lot of differential…
Introduction When doing mathematics, we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive. Going from rational numbers to reals is more complicated. The easiest way at the start is probably infinite decimals. Dedekind Cuts can be used to get a bit more fancy. A Dedekind cut is a…
Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say 1/trillion to the power of a trillion) can be thrown away because they are negligible. That way, when defining the derivative, for example, you do not run into 0/0, but when…
Abstract There is so much to say about the many endeavors by professional scientists to explain to us the world. The list is long: Carl Sagan, Harald Lesch, Neil deGrasse Tyson, Sabine Hossenfelder, Michio Kaku, and I even saw Roger Penrose and Steven Hawking on tv. The list is – of course – considerably longer…
A central principle of Physics Forums regarding homework help is not to provide solutions on demand but to guide students along a path to the answer. The rationale behind this principle is articulated in the familiar saying, “If you give a hungry man a fish, you feed him for a day; if you teach him…
Introduction A commonly encountered school-level Physics practical is the determination of the internal resistance of a battery – typically an AA or D cell. Typically this is based around a simple model of such a cell as a source emf in series with a small resistor. The cell is connected to a resistive load and…
I often read questions about our classification scheme that we use on physicsforums.com to sort posts by science fields and subjects, what has to be studied first in order to learn something else, what is a good way through physics or mathematics in self-study or simply about the desire to understand, e.g. general relativity…
If you are interested in programming and electronics, you probably do not need an introduction to Arduino. If you want to make your Arduino projects permanent, then it is a good idea to use solo microcontrollers rather than Arduino boards in the final setup. While Arduino boards are great for prototyping, buying an Arduino board…
Two of my favorite areas of study are linear algebra and computer programming. In this article I combine these areas by using Python to confirm that a given matrix satisfies the Cayley-Hamilton theorem. The theorem due to Arthur Cayley and William Hamilton states that if ##f(\lambda) = \lambda^n + c_{n-1}\lambda^{n-1} + \dots + c_1\lambda +…
What is the ambiguous case? In high school geometry, the idea of proofs is often first introduced to American students. A common task is to use a basic set of rules to prove two triangles are congruent, which is a fancy way of saying they have the same side lengths and the same angles. Phrases…
Confessions of a moderate Bayesian part 3 Read part 1: How to Get Started with Bayesian Statistics Read part 2: Frequentist Probability vs Bayesian Probability Bayesian statistics by and for non-statisticians https://www.cafepress.com/physicsforums.13280237 Background One of the things that I like about Bayesian statistics is that it rather closely matches the way that I think about…
I have written many Insights (and coauthored an entire book) explaining how the puzzles, problems, and paradoxes of modern physics can be attributed to our dynamical bias and resolved by rising to Wilczek’s challenge [1]: A recurring theme in natural philosophy is the tension between the God’s-eye [4D] view of reality comprehended as a whole…
We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many great responses we need to split them into parts, here are the first several. This is part 3. Read part 1 here and part 2 here. Enjoy!…
We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many great responses we need to split them into parts, here are the first several. This is part 2. Read part 1 here. Enjoy! gleem AI:…
Today we get to know a little more about Engineering Mentor jrmichler! Tell us a bit about your education and academic years Two years college (UW-Madison) in electrical engineering. Burned out (two semesters of 21 credits, tired of poverty, needed to think some things through), dropped out, joined US Air Force. Four years later, had…
Introduction to Evolution The study of evolution has dominated the field of biology for over a century. Explaining why the life we see is as it is fascinating scientists and non-scientists alike. Thanks to this fascination there are a number of questions that often come up about evolution; this primer contains some FAQs, key facts,…
The Google Doodle for 2 February 2020 celebrated Mary Somerville, the Scottish polymath and science writer, and with Caroline Herschel, the joint first-ever woman to be made an honorary member of the Royal Astronomical Society. Born in Jedburgh, Scotland, in 1780, Somerville received little formal education compared to her brothers. Largely self-taught, she pursued academic…
People often claim on Physics Forums and in the foundations community proper that quantum mechanics is “incomplete.” Indeed, Lee Smolin recently wrote [1, p. xvii]: I hope to convince you that the conceptual problems and raging disagreements that have bedeviled quantum mechanics since its inception are unsolved and unsolvable, for the simple reason that the…
Introduction The student of thermodynamics, as they consider pistons and ideal gasses and such, often begin to grasp the nature of entropy only to find as they delve deeper that grasp slips away. In the deeper analysis of thermodynamic systems via statistical mechanics this grasp may slip away entirely. “How can my cup of hot…
Definition/Summary A Lie algebra (“Lee”) is a set of generators of a Lie group. It is a basis of the tangent space around a Lie group’s identity element, the space of differences between elements close to the identity element and the identity element itself. Lie algebras include a binary, bi-linear, anti-symmetric operation: commutation. The commutator…
This is the first of several posts that will develop some mathematical machinery for studying Fermi-Walker transport. In this first post, we focus on Minkowski spacetime in order to introduce the basic concepts without having to deal with the complications introduced by spacetime curvature. Before looking at Fermi-Walker transport, we first need to introduce the…
Part III: Representations 10. Sums and Products. Frobenius began in ##1896## to generalize Weber’s group characters and soon investigated homomorphisms from finite groups into general linear groups ##GL(V)##, supported by earlier considerations from Dedekind. Representation theory was born, and it developed fast in the following decades. The basic object of interest, however, has…
Introduction In the first part of this series, I talked about some fundamental notions in the world of algorithms. Beyond the definition of an algorithm, we saw the criteria, ways to represent an algorithm, the importance of correctness, and elements of the classification and analysis of algorithms. It has also become evident that it is…
Give us an executive summary on bhobba I was born in Toowong Brisbane Australia 17/11/1955, and was raised in suburbs around Toowong – Toowong itself, Taringa and Indooroopilly. I went to 3 schools Taringa State School,. Toowong High and Indooroopilly High. I now live in Redland Bay Queensland Australia. It is about halfway between Brisbane…
Many threads here at PF include some questions about how to learn to program. This is asked by Physics students who want to learn programming in order to help their study, work on some project or create some simulation among other things but also by students in other fields of science and by other members,…
The terms Bizarro and Bizarro World originated in Superman comics, where strangely imperfect versions of Superman, other action characters, and even Earth itself were conceived of, and provided the basis of stories. And who can ever forget the Seinfeld episode entitled “Bizarro Jerry,” in which there are Bizarro versions of Jerry and all his friends?…
Clifford V. Johnson is a professor in the Physics and Astronomy Department at the USC. “I mainly work on (super)string theory, gravity, gauge theory and M-theory right now, which lead me to think about things like space-time, quantum mechanics, black holes, the big bang, extra dimensions, quarks, gluons, and so forth.” Clifford V. Johnson runs a…
Give us an early bio on yourself Well, I was born and raised near Dallas, Texas as the only boy of 4 children. I grew up with 3 sisters, though I had another sister, 3 stepsisters, and a stepbrother that I did not live with. I’m only 10 minutes younger than my twin sister…
This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METU Previous Chapter: A Journey Into the Cosmos – The Friedmann Equation Chapter 2- FLRW Metric and The Friedmann Equation In this chapter, we will further investigate the Friedmann equation and we will…
This is the first of a multi-part series of articles intended to give a concise overview of statistical mechanics and some of its applications. These articles are by no means comprehensive of the entire field, but aim to give a clear line of reasoning from Boltzmann’s equation to non-equilibrium statistical mechanics. It is hoped that…
This article is part of our student writer series. The writer Arman777 is an undergraduate physics student at METU This is an introduction to cosmology for someone who has some knowledge of calculus and basic physics. In this tutorial, we will take a journey into the cosmos to study cornerstone ideas in cosmology and their…
Please give us a brief background on yourself Over 40 years ago, I studied mathematics, physics and computer science in Freiburg and Berlin (Germany). My Ph.D. thesis was in pure mathematics, but I was later drawn more and more into applied mathematics. Since 1994 I am a full professor of mathematics at the University of…
This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 8. Phase space. The next chapter is 10. Gauge symmetries. 9. Propagators In this chapter we discuss the following topics: Background Fourier analysis and Plane wave modes Microlocal analysis and UV-Divergences Cauchy principal values Propagators for the free scalar…
Introduction It is surprising that the homopolar generator, invented in one of Faraday’s ingenious experiments in 1831, still seems to create confusion in the teaching of classical electrodynamics. This is the more surprising as the problem of the “electromagnetism of moving bodies” has been solved more than 100 years ago by Einstein in his famous…
This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 4. Field Variations. The next chapter is 6. Symmetries. 5. Lagrangians Given any type of fields (def. 3.1), those field histories that are to be regarded as “physically realizable” (if we think of the field theory as a…
The CMB establishes a record of ancient acoustic oscillations in the baryon-photon plasma. We’ve been studying how these primordial sound waves evolve, and how to analyze the last scattering surface to learn about them. Now it’s time to confront their origin: what process composed the cosmic symphony? A few different proposals have been advanced…
Key points The author begins by questioning the nature of numbers and their deeper significance. Numbers can represent various mathematical constructs, from scalars to linear mappings of one-dimensional vector spaces. These numerical representations can be described as elements of fields, dual spaces, and matrices. The concept of tensors is introduced, which are multi-dimensional arrays of…
Please give us a bit of background into your educational and professional life. I’m a public school kid through and through. After going to the local high school where I grew up in Westford, Massachusetts, I attended Michigan State University to get Bachelors degree in astrophysics (with several extra classes in Computer Science). From snowy…
Undergraduate interest in research is a good thing; it’s even better if they aspire to publish their work for review and consideration from a broader audience. First, we should consider what it means to be publishable. Usually, “publishable” means a paper contains a novel and interesting result in either theory or experiment that is more…
Quantum Mechanics(QM) is one of the greatest intellectual achievements in human history. Not only because it describes the world at the microscopic level and in turn, provides us with the technological advancement that we enjoy today, but also because it shows us how little we know about the world we’ve been living in for so…
We are please to introduce our newest member of the mentor group, fresh_42! Can you give us a brief bio? I studied mathematics and economy and always worked in the periphery of IT. Often as a programmer on various platforms and in various languages, but as well on a hotline, as a software designer, project-,…
In this Insight, I’m going to talk about two of the first science experiments in recorded history. One was allegedly performed by the Prophet Elijah in Israel in the 800s BC [1], the other by the Pharaoh Psammetichus in Egypt in the 600s BC [2]. In each case, we only have one primary source from…
Read part 1 -Backyards, Barns, Bayous When I was offered a job at the Air Force Academy, it seemed like an opportunity to exercise both my commitment to academic rigor and my desire to serve my country while continuing with the basement and boat ramp approach to research. Since I was faculty in the Department of…
Introduction It is a remarkable fact that consideration of very elementary concepts in geometry often leads quickly into deep and unexpected mathematical terrain. In high school and even college, such complexities are usually treated cursorily or omitted altogether, in order to avoid bogging down coverage of the essentials. In this article, we delve, at least…
This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles”, “Misconceptions about Virtual Particles“ , and ”The Vacuum Fluctuation Myth”, which make precise what a virtual particle is, what being real means, document some of the liberties taken in physics textbooks in the use of this concept, mention the most…
First of all: What is a representation? It is the description of a mathematical object like a Lie group or a Lie algebra by its actions on another space 1). We further want this action to preserve the given structure because its structure is exactly what we’re interested in. And this other space here should…
For those who don’t know the great David Hestenes, he is the inventor of the geometric algebra formalism of physics. Here we go! 1) What is the best application of geometric algebra in theoretical physics that you can think of? In other words, what application shows the power and elegance of geometric algebra best? The…
We are pleased to introduce David J. Griffiths. Professor Griffiths is one of the most successful physics textbook writers. Odds are if you studied physics in college, you’ve used one of his textbooks. We are pleased and honored to obtain some of his insights on the quantum and academic world. Here we go! Please give us a…
The Connes-Lott-Chamseddine-Barrett model is the observation that the standard model of particle physics — as a classical action functional, but including its coupling to gravity and subsuming a fair bit of fine detail — may succinctly be encoded in terms of operator algebraic data called a “spectral triple”. This involves some non-commutative algebra, and…
At first, I wanted this title to say “Ohm’s law is not a Law.” But someone else used that phrase in a recent PF thread, and a storm of protest followed. We are talking about the relationship between Voltage between two points in a circuit and the current between those same two points. ##R=V/I##, or…
I posted this elsewhere (on my personal blog), and someone mentioned that maybe it might also be useful here on PF. So I’m reproducing the entire entry here in case it might make a difference. This is essentially a “sequel” to my earlier essay on “So I am Your Academic Advisor“. My aim in writing…
Key Points DNA is a good model system for polymer physics as it is small enough to observe single–molecule dynamics and large enough to be thermodynamically driven When DNA is coiled in the cell nucleus, it has no direct correlation between spatial position and genetic position When stretched out in a nanochannel, there is a…
Give us a little background on yourself? I was born in Washington DC, grew up in Texas, bachelor’s in physics from Harvard in 1978 but found a career in system software instead. Son of two law professors and grandson of a third, raised a Quaker although it didn’t stick, keep a small fleet of well-rusted…
Three million years ago, the grandfathers of our genus used sharpened stones to chop wood and cut bone. Today, surgeons use fiber optic-guided lasers to clear microblockages in the heart. Within our own lives, we’ve gone from burning our mouths on hot soup as children to cautiously blowing on the first spoonful as adults….
This insight is written for high school students who don’t feel very challenged by their high school courses. Or maybe those high school students who want to have a taste of what university math is like. The good news is that you don’t have to wait until university to see exciting mathematics, you can learn…
Is it possible to design an unbreakable cipher? Do methods of encryption exist that guarantee privacy from even the most capable and highly-resourced of prying eyes? This question is especially relevant today, as individual privacy and national security increasingly find themselves at opposite ends of the arbitration table. Powerful nation-states with unparalleled mathematical know-how and…
Abstract Over the past few years, the author and his wife have served as teachers, qualified scientists, mentors, and/or parents on dozens of science projects assisting students ranging from elementary school projects that can be completed in a weekend to high school and college freshmen projects that take a semester or year to complete and…
Please give us a bit of background on your life and professional experience Life: Born educated in Italy, then 10 years in the States and 15 in France. I got to physics late: before I was more into the hippies dreams or trying to overthrow the Italian government. Professional: in my third university year I…
We are proud to introduce you to Mathematical Physicist and PF member John Baez! Give us some background on yourself. I’m interested in all kinds of mathematics and physics, so I call myself a mathematical physicist. But I’m a math professor at the University of California in Riverside. I’ve taught here since 1989. My wife Lisa…
A monographic substitution cipher works by replacing individual characters of plaintext with corresponding characters of ciphertext. It is perhaps the simplest encryption scheme ever devised: early monographic substitution ciphers were employed by Julius Caesar to secure private correspondence. These ciphers were low-tech, required virtually no mathematics, and encryption and decryption could be accomplished by finger…
Can you give us a brief history of berkeman? I grew up in a military family (my dad was an Army colonel), so we moved all over the place when I was a kid, finally settling in Calistoga in the northern part of the Napa Valley, California, for my high school years. Being a military…
Give us a brief history of Borek Note: text below is of a negative pedagogical value, don’t read it if you are younger than 20, attending school or still naïvely hoping for the best. I was born half a century ago, in a galaxy far, far away. So far away our laws were all shifted…
This is a new Interview category for Insights. While I line up some great new interviews I’ll be migrating some previous mentor interviews. Doc Al is a physics mentor for Physics Forums Can you give us a brief bio? Okay. It was never easy for me. I was born a poor black child. I remember the days,…
What causes cancer? For the most part, cancer is a disease that arises from mutations in the body that accumulate over time. These mutations knock out key tumor suppressor genes involved in repairing DNA or regulating cell division and activate oncogenes that can drive cells to divide uncontrollably and invade other tissues. But where do…
Motivations for creating the series I came to Physics Forums originally to read ZapperZ’s thread about becoming a physicist back in 2013. It was one of many factors that got me to pursue an education in physics that I am succeeding to this day. One thing I wanted to find here that didn’t seem to…
Key Points Funke and Dietz created a DNA hinge which is adjustable by varying the length of one of the DNA molecules, allowing positioning of molecules attached to the hinge by as little as 0.04 nanometers. DNA origami was one of the first successful methods of “bottom–up” nanotechnology, allowing structures such as cubes, smiley faces,…
Before proceeding with a discussion of the super p-brane sigma models, whose emergence from the superpoint I discussed in the previous article, we need to speak a bit about the fundamentals of local Lagrangian field theory in general, of which these sigma-models are examples. The geometry that underlies the physics of Hamilton and Lagrange’s…
Doubt, as odd as this may sound, can actually be essential to our living. We all make decisions and later have questions on whether we made the right choice or not so doubt will help influence our next decision when it comes to the same question or choice. While doubt is a natural part of…
It’s 6:30 in the morning. You’ve just woken up and you feel so sleepy you think to yourself “A few more minutes can’t hurt.” And so you drift on to sleep under your warm comforter. The sounds of kids playing outside, mixed with the sunlight and birds chirping at your window wakes you up three hours later….
Is spacetime really a continuum? That is, can points of spacetime really be described—at least locally—by lists of four real numbers ##(t,x,y,z)##? Or is this description, though immensely successful so far, just an approximation that breaks down at short distances? Rather than trying to answer this hard question, let’s look back at the struggles…
Introduction It is a common saying that during inflation “space expanded faster than the speed of light.” This statement is meant to articulate the extreme rates of expansion seen during inflation, and this it does successfully. Unfortunately, it is at least a little wrong, and what little there is right about it is not unique…
My goal in this article is to derive a simple equation for the proper acceleration of an observer traveling on a circular path around a Schwarzschild black hole at some constant radius [itex]r > 2M[/itex]. (Note that this is not the same as being in a stable circular orbit about the hole; we allow for…
I am going to backtrack a little bit and talk about writing your Curriculum Vitae (CV) and what you should focus on in search of a job in physics. This includes looking for a Postdoctoral position, a research position, and possibly a faculty position at a university. I am going to base this…
If you intend to pursue an academic/research career, chances are, you will need postdoctoral experience. This is typically a 2 to 3-year appointment either at a university, national laboratories, or industrial laboratories such as Bell Lab. It is not uncommon for someone to do 2 postdoctoral positions before finding suitable employment. So this…
At this stage, you have performed your doctoral research work, maybe even have published (or about to publish) a paper or two, and may have presented your work at a physics conference. It is time for you to think about finishing this part of your life. However, before you can do that, you…
I mentioned earlier that there are two ways for physicists to communicate their work. The first is via publications in peer-reviewed journals. I have covered this in the last chapter of this series. The second, which we will cover here, is through oral presentations at various scientific conferences. Each year, there are scientific…
At this stage, you are well into your Ph.D. research work, and depending on what area of physics you are in, you may already start producing new results. This next part of the series will cover an extremely important aspect of your graduate work that is typically not covered (sometimes not even required)…
Now, where were we? Oh yes! You have now started with your actual research work. You and your adviser have agreed on at least the general type of area you will be working in and you have started to do a lot of literature search of what is going on in that field,…
News of the LHC progress has dazzled scientists and hobbyists alike. It’s now time to show just how much you know about the operation. Please share your results Ready for your next quiz? How well do you know about the Periodic Table of Elements? 1. What is the Large Hadron Collider (LHC)? The Large Hadron…
You are now entering your first year of graduate school. In terms of the academic aspect, you will have a set of required courses that you must take. Typically, these courses would be advanced classical mechanics (at the level of Goldstein), advanced QM (at the level of Merzbacher and Sakurai), and advanced E&M (at…
We are still discussing the final year of your undergraduate education. So far, we have covered what you need to consider if you want to go on to graduate school and prepare yourself as best as you can for that part of your journey. This is the “traditional” path that many physics students…
We have now reached the final year of your undergraduate program. By now, you would have gone through courses in the fundamental pillars of physics (Classical mechanics, Quantum mechanics, and E&M), and even courses in Thermodynamics/Statistical Physics. Academically, this is where you start taking more advanced courses, even some graduate-level courses. There are plenty…
So far, I have covered what I believe a student needs all the way to the end of the 2nd year of studies. In most schools in the US, an undergraduate must have a declared major by the end of the 2nd year (if not sooner). So by now, you should already be officially…
Part III: Mathematical Preparations In most universities in the US, a student must have a declared major by the end of his or her second year. So this is an important transition – making the commitment in a particular area of study. By now, if you have followed the first two chapters of this…
Part II: Surviving the First Year of College This part covers the survival tips of the first two undergraduate years. So now you’re in college, and you have every intention to be a physics major (actually, what I’m about to describe applies to anyone who is taking a physics class, not just for physics…
Introduction There are many sins in physics didactics. Usually, they occur, because teachers, professors, textbook or popular-science-book writers, etc. try to simplify things more than possible without introducing errors in reasoning, or they copy old-fashioned methods of explaining an issue, leading to the necessity to “erase” from the students’ heads what was hammered in in…