Don’t rob the self-learner that doesn’t have access to TAs, fellow students, and professors the ability to check their work, just because someone else doesn’t have the discipline to not abuse it.
Textbook solutions are good for those that aren’t in school, aren’t in formal programs and have no other way of receiving feedback.
The “you should know if you’re right” mentality doesn’t necessarily fit a person that’s been working for 10-years and has been out of the academic mindset. One that is a beginner and could easily fool themselves into thinking they have a correct answer.
It doesn’t allow for correction of false thinking. Anyone can think their proof is correct. But fewer beginners can properly recognize when they are wrong.
This sort of mentality is a bit elitist and gate keeping.
I had a girlfriend who was doing her PhD in Physics. I remember one night she and her classmates spent all night working on a problem, that was essentially unsolvable. The next day they go to class and all of them made their best attempt, but no one could complete it. The problem? The professor accidentally used the wrong metric on one of the numbers meaning that they couldn't do the steps to what should have been an easy solution. Now they noticed this, they are a smart group of people, but that's not what the problem was, so they spent hours and hours trying to solve what he gave them without any hope of actually doing it.
In the end, he was like "Oh my bad," and corrected his mistake. The point of the story is that they were able to essentially ask him for the solution and they were able to check what they'd done, and in the end he made the mistake. In situations like this, he should provide the answer if nothing else to show that he didn't make a mistake in the problem set. People are fallible, no matter how brilliant you are.
I had a similar thing happen in high school physics. We were were suppose to figure out where and when a projectile was going to land. The only problem was that it was never going to land—-the initial velocity was too high.
In retrospect I think it was a great lesson for my future career as a data engineer. Doesn’t matter what the source is, any datum can be just plain wrong.
That professor probably had produced the answer already, using the metric he had initially intended. Having a set of answers doesn't mean you didn't make a mistake in the questions.
There's a story of a prof injecting one error into every test.
I had a industrial engineering teacher that did something similar. Every team had a (fake money) budget for each project and bought materials from him (sole source). He'd randomly cut corners, to keep everyone on their toes. Good lesson for the real world.
On the other hand, struggling all night to solve an un-solvable problem is a valuable learning experience, too. In the real world we struggle all the time with problems that don't have solutions.
I took a quick look through the first set of exercises and a lot of the problems are open-ended and don't have specific answers. Seeing a different answer than yours doesn't tell you much about whether your answer is correct.
Even if you do have a similar proof to the one in the answer key, that doesn't mean your proof is correct. Correctness can often hinge on very subtle distinctions. You really need a TA or instructor to read your proof if you want meaningful feedback.
As I've said elsewhere, I'm looking out for my own students first.
One of my colleagues suggested setting up a "club" on PerusAll (https://app.perusall.com/welcome) or something similar that would allow people to discuss to book and/or work through problems collectively. (They have a club for CLRS, for example.) Right now all their "clubs" are restricted to books with Reputable Publishers (ptui), so they might need some persuasion.
Presumably nothing's stopping you from putting a book of solutions and posting them online. It seems like a much easier task than writing this book, with all its problem sets, and then posting it online for free for the world to read.
It might be an elitist and gate keeping mentality but I have to say that calling providing a free resource to someone, but not tailoring it to fit their exact situation, "robbing" is a very entitled one.
How is it just a choice of living in a poor area vs a rich one? What if the people living in the poor areas don’t even have a high school degree? Can they suddenly decide they want to work and live in the rich area?
I’m a couple generations maybe. Moving from a poor area to a rich one and working your butt off for your kid’s education so they can reach professional successes you didn’t have the opportunity to is an archetypical immigrant story.
I'm convinced this is just another Protestant work ethic as secularized by capitalism, ala Max Weber. Each generation is supposed to work hard and devote everything (or almost everything) so their kids have it better, but who gets to say, I have it better, I'm not going to work hard anymore, so I can enjoy some of it? How the public general treats people who have amassed enough to live on but don't actively have a job, seems a testament to the religious foundations and origins of the idea, rather than anything drawn from what might be called reason.
It's not "move to a rich area". It's "move to an area with good opportunities for production (roughly 'good jobs', although self-employment is also a possibility of course)". That's a very different problem. An area with high cost of living, almost by definition, has a lower margin of production and thus lower real incomes for such, adjusting for productivity.
Well, until the rent seeking class figured out how to asset inflate the education and property market. If you look at exploding debt levels in property, education, housing, and personal credit something is extremely broken and shoving everyone in the big city is not the long term answer unless we are looking at some massive social upheaval in the near term.
Now that communication is quick, and data more available, more people have an idea of how to give themselves the best opportunity. The best school district you can send your kids to, the best colleges they can go to, the majors they can study, etc.
Problem is it's all concentrated to a handful of options, so everyone is chasing after those, and the sellers know it so they can price it such that almost all the value is extracted from the buyer.
It's funny to think that it could partly be a consequence of all the easily available school rankings, all the way form elementary to university, as people can sort themselves by socioeconomic class much easier. But it could go the other way too, with the concentration being a consequence widening gaps in socioeconomic class. Either way, it feels like a feedback loop to me.
True, but that applies to rural areas as well: how many farmers are renting their land these days, or are working for big farm corps that bought all the family farms in the area a long time ago?
- It's an MIT graduate class (this could be a con if you are a beginner in other areas and not just in quantum computation).
- It's taught by Isaac Chuang (of Nielsen & Chuang, the leading textbook on quantum computing) and Peter Shor (of the Shor factoring algorithm, the most famous quantum algorithm).
Cons:
- Shor does 90% of the lectures, and he is... not a good teacher.
- When I took it, there was almost zero support (e.g., when there were bugs in the problem sets).
I'm glad I took it, because it induced me to learn a bunch of material I had been wanting to learn for a while, but compared to what it could have been it was pretty disappointing.
I’m apprecticative of the amount of work and effort you put into the book. Please consider the self-learner and those that don’t have access to solutions, a classmate, a TA, or a professor.
I know you probably don’t want to expose solutions to the exercises so they can be used in a classroom, but for people like me, I don’t want to create an online discussion to every problem I attempt just to check my work.
I prefer to read textbooks that have solutions, so I can know for sure my answers are correct.
I don’t really buy the “you know when your solutions are correct”. The beginner can easily fool themself into thinking their solutions are correct, when they aren’t.
That's cool -- you might like Underwood Dudley's book on Elementary Number Theory. It has a similar set of topics, and I think it has more exercises and contains some solutions. And it's inexpensive!
I'm on the same boat as you. I might still buy this book, it seems beautiful.
In the days of online autodidactic zeitgeists, it's a shame not to include the solutions. I understand the author wants to monetize his hard work and ensure it'll make money as a textbook and I believe textbooks can provide some income as long as they become the mainstay of a particular subjects.
That being said, I wonder if there is a future option for creating a problem/solution booklet exclusive for the teachers and opening up the solutions to this book so the entire world could possibly learn from this book.
Yes -- that is a future option. It's a time commitment, but perhaps next summer I'll post a new section on the book webpage with more exercises and solutions to existing ones. (Those who have taught with the book asked for more problems too.)
This looks great, but are solutions provided? Books like this are almost worthless for me to self-study since I don’t have access to a classroom or professors and no way to check my solutions.
It's a nice book, but I wouldn't use it for study or as a textbook. And solutions are not provided as far as I can tell. I'm afraid you're going to have a difficult time finding books which contain solutions to their problems.
Thanks. I won’t bother buying it then. Do you have any recommendations on good math books to work through on my own that have solutions floating online, so I can check my work? I’m looking for a theoretical math book to work through. Primarily looking for intro to proofs or algebra related books. But anything will do. I just want something proof-y aimed at beginners.
Polya & Velleman are classics. They're about problem solving & proof writing techniques, but won't teach you any abstract math. I've only ever heard good things but i've actually never read them myself! Some other suggestions:
Niven - The Theory of Numbers. Contains hints for some of the proof based exercises, and answers for many of the computational exercises. I used it for my undergrad course, I remember it being reasonably beginner friendly.
Pressley - Elementary Differential Geometry. Has terse answers to every exercise! The subject is a nice mixture of concrete and abstract, calculation and proofs, and there's some interesting work using differential geometry in CS via computational geometry. Also i think it's used in robotics and a few other things? This book is very beginner friendly, it will get you about 1/2 way to General Relativity.
LibGen appears to have instructor's manuals for several common non-honors texts, including Fraleigh and Gallian (abstract algebra), Rosen (number theory), and Bartle/Sherbert (analysis).
Easy for you to say as an outsider with a comfortable salaried job. A lot of people in these rural communities aren't educated and live paycheck-to-paycheck. Putting them in larger cities for jobs they aren't qualified and wouldn't be hired for probably isn't the solution.
Indeed. But the skills mismatch is one of the things I am proposing to address. People can be retrained, at least if they're on the younger side. Trying to retrain a 55 year old factory worker whose employer moved the plant to Mexico or China probably wouldn't work too well. It might be better to let him retire early.
>Putting them in larger cities for jobs they aren't qualified and wouldn't be hired for probably isn't the solution.
<tinfoil>
If your goal is to make rural people (historically a very hard group for governments to control, everywhere, not just in the US) more dependent on and controllable by the state then it works great.
</tinfoil>
(Yes, I know I'm just stirring the pot by saying this)
All a man needs is a horse and a gun and he can rule the world, right?
I know many rural Americans like to imagine they're still living on the lawless frontier uncorrupted by civilization and Federalism, but.... it's not actually true that they're less dependent on the state than "city folk." Hell, in many cases rural areas are more dependent on the state.
And ironically, it's that pastoral, romantic delusion of the statelessness of rural America that leads to the very same populist ideology that makes them easier to control. Like believing a billionaire globalist with a history of exploiting low wage employees and a loose relationship with the truth is an honest, God-fearing hard working friend of the common man.
> it's not actually true that they're less dependent on the state than "city folk." Hell, in many cases rural areas are more dependent on the state.
I'd like to see you back up this claim, but either way dependence on "the state" isn't really what matters.
What matters is the interdependence between the two locales. Cities are almost entirely dependent on rural areas for their food. Rural areas could continue to exist without cities; the reverse is not true.
Cities are also more fragile than rural areas. Say something catastrophic were to happen to some region of the US, something that wiped out communications infrastructure, electricity generation, supply routes (roads, rail), etc. The cities in this region would be foodless within a few days. Depending on the city, there would be either no running water or dirty running water. Even if martial law were quickly instituted, violence and starvation would result.
Contrast this to the rural areas. Food would certainly be an issue, but it is more likely that the population is either (a) near agricultural infrastructure or (b) prepared to fish/hunt/forage. It helps that there are less mouths to feed.
Furthermore, most people are on wells and/or septic tanks, which barring damage gives them a much longer timeline before water/sanitation becomes an issue. Again, it helps that there is a lower density of people needing drinking water and sanitation.
I guess my ultimate point is that strategically, it is the rural areas holding the cards. Would they be poorer without the cities? Absolutely. Could they survive? They did for generations.
There are very few rural areas in the US in which most people don't get their food from the supermarket, water from utilities and power from a power company, just like everyone in a city. They didn't build their homes from trees they felled by hand, they don't grow their own food, or sew their own clothes.
As far as hunting and fishing goes, few people living in rural areas would be capable of living entirely off the land for an extended period of time, so the premise that they would be able to survive a disaster more or less unscathed while the city dwellers starve is just really not true, at least not as true as Americans would like to believe.
One problem rural areas do have is lack of disaster preparedness funds. I live in Texas, and I've seen what happens when disasters hit rural areas. The same people who complain about Washington and city dwellers wind up in tent cities being tended to by the Red Cross and FEMA.
See how well agricultural communities do without farm subsidies, housing loans or food stamps. Without the state keeping them alive, a lot of them would simply die out.
And this is my ultimate point - most Americans who live in rural areas are little less domesticated than their urban counterparts.
There is a lot of talk about elite universities offering full-tuition to those that make under a certain income, but what this ignores is usually you have to be in a certain income bracket to obtain certain SAT, AP scores along with the right ECs and upper division college prep courses. This usually means attending the best private, public, or STEM magnent school in your state, which sadly most families in those income brackets cannot afford. The people getting into these elite schools come from elite secondary schools and the poor people that can't attend these schools are usually excluded from admissions to elite colleges. So the "free tuition" advertisement is nice, but in practice their admissions standards do a good job of keeping such poor folks out.
This is at best a half truth. Going to these schools helps, but it is not necessary.
There are an abundance of people who are qualified to get into elite universities at less-than-best schools in a given state.
There are three main issues that I see:
1. They self-select out of applying. They know lots of smart people, but they don’t know anyone else who applied, so those elite schools must be impossible to get into.
2. Their teachers/administrators have no idea how to write a strong recommendation for a stellar student. The applicants don’t know how to choose people who can write good recommendations.
3. The applicants don’t know about the small tweaks in their extracurriculars that will make them standout (e.g., demonstrating leadership, vision, etc.), and/or they don’t know how to write about their considerable achievements in a compelling way (e.g., I’ve heard an incredible and incredibly modest person saying that their considerable achievements were not worth discussing on an appication because “Well, what else would you do? Isn’t this just normal?” Answer, no, it was not normal.).
Note also that plenty of the “poor” students have been recruited in one way or another, with athletes probably being the biggest recruiting pool.
I think the admissions practices are largely fine, and they dont, by design, aim to keep poor people out (as you suggested).
I think that these schools could do a better job at educating potential applicants and the circle of people around said potential applicants much better. In my opinion, the internet has democratized this process considerably over the past 20 years or so, but I think there is still considerable room for improvement, especially by the universities themselves.
I guess I'd disagree, in that admissions practices at many schools are designed to admit children of rich people. Sure, poor people aren't penalized for being poor per se, but they're not going to contribute to the endowment, you know?
So you get a boost for being a legacy, for having parents who are rich, for being from a rich feeder school that indicates you have parents who are rich, etc. It's not that you get a -1 on your point total for being poor. It's that you get a lot of +1s for being well-off, because ultimately well-off people give more money back to the school & produce well-off alumni who are attractive to well-off applicants. At private colleges and universities in particular there is a careful attention paid to long-term revenue, as colleges are feeling the economic squeeze in the amenities arms race. Colleges are separating into 'winners' and 'losers' and that sorting is along the lines of revenue and endowment.
The article is right on that connecting unconnected kids with connected peers is the biggest benefit of an 'elite' education. 'Winner' colleges today are trying to surf the wave of existing power structures rather than create/educate a new wave of potential elites.
I worked at a well-known Texas college for a few years in the IT department. I can tell you first hand they overcharge. Tenured professors are largely lazy. They are paid enormous sums of money for as little as 4 hours' work daily. The adjuncts work their tails off and while they are making 75k+, the whole thing is a sham. Let's not talk about incoming students with credits from other institutions who are like 4 credit hours short and they make them take a full year or more (because they can), and charge out the wazoo and think you should be grateful.
Working for this college let me know one thing: those who can't, teach. More than once I had to step in and assist the CS professors with basic things they should have known. Tenured professors whose CV read like they must have been there at the epoch and worked with Dennis Ritchie and Ken Thompson.
In addition access to exclusive and expensive sports, if you have the money, some easy tickets into the Ivy League include: fencing, sailing, rowing (crew), lacrosse, golf, tennis and equestrian.
And if you don't have the money, being elite at any other sport will do. Soccer, basketball, football, track, etc.
A run of the mill guy or gal with a straight A record and shooting 60% from three will find a ready welcome at Stanford. That same run of the mill straight A student would be laughed out of the room if they applied without the elite basketball skills. Your daughter might not have much of a chance as a simple straight A student, but if she has straight A's and runs a 48 or 49 second 400... yeah... I can guarantee you that they'll make room for her.
If you're talking about using sports to get in, then almost any sport will do, you don't have to have money for the expensive ones. Problem is, you kind of have to be elite to make it work. Four year varsity starter, state champion level basically.
> Problem is, you kind of have to be elite to make it work. Four year varsity starter, state champion level basically.
Maybe at Stanford. Maybe at Ivies in certain highly competitive sports (e.g., rowing).
In most sports, simply being a recruitable athlete at a level lower than “power conference” but higher than NAIA (maybe?) is possible depending on the sport and/or specialty. In terms of skill, any high school with 1000+ students probably has 10-50+ students in this category — grades and/or lack of desire are often holding them back from a tertiary education of any kind. Said another way, that’s much lower than “state champion” level.
Again, knowing how to get recruited and having a coach who knows how to showcase talent for recruiters goes a long way. That said, it only helps, but is not required in most sports.
I’m really glad you mentioned running as an example. There are a ton of good track & field and cross-country folks who: 1) can improve significantly just by training well, and 2) are very recruitable at the Ivy League level. Want-to goes a long way.
It is not mandatory to be in a certain income bracket to get a high score on your SAT or on your AP exams.
If the universities want to help low income students, and are only able to help a certain number of them given the resources they have available, academic merit is the best way to do it.
It isn't mandatory, but it certainly helps when you can pay for private tutors or professional consulatants that craft your application package. Students that tend to score high on SATs tend to come from higher income brackets. It also hurts when you attend a school that doesn't offer an expansive list of AP courses, or if you come from a family that never attended college and do not even know what the college process is like.
Edit: To your "This is patently untrue" comment. Taking AP courses and scoring 5s on the exams is pretty standard for applicants getting into elite colleges. By not taking those courses you are huritng yourself when applying to such places.
I worked at a small liberal arts college for a few years that basically admitted (1) legacy students, (2) rich kids, (3) sports kids from the South (from states with no D3 football, basically), and (4) poor kids who got high SAT scores. They used (1) for history, (1) and (2) for revenue, (3) for school spirit, and (4) to boost the average SAT for the whole student body.
So many schools are doing exactly what you suggest. It is kind of weird to teach there & realize pretty quickly that the rich kids are mostly not the smart ones, to be blunt.
Have to be? Or tend to be. I think we often overlook that richer families tend to have a lot better parenting. It's not just about money. Good parenting is arguably more important than being wealthy.
Having money to throw around makes it a lot easier to be a "good" parent.
I grew up helping my dad with every project around the home. Economics improved over the course of my childhood and my much younger brother spent his after school time playing sports and musical instruments. He got to put that on his college applications. "Dig's a good fence post hole" is not something you put on a college application. I went to the state school that gave me the best aid. He got an almost full ride at an exclusive liberal arts college. His side projects during college were audio related. My side projects involved parting out vehicles. When you're interviewing for an entry level job at FAANG and they ask you to tell them a little bit about yourself talking about how you do custom speaker enclosures is probably a good choice. Talking about your side gig selling used car parts will get blank stares if you're lucky and make you look like white trash if you're not. We'll see what he does after college but I suspect he'll be doing better than me by the time he's 30.
Having enough money to give your kids a marginally higher class upbringing from day 1 makes a world of difference.
Has Professor Hinton ever made a known appearance on HN?