thanks for your hard work. I love the rigourism that you enforce in your videos. I am working on my english, thanks again. I engage my kids to study mathematics with me, I just found the Modern Algebra book 1 that you showed the other day to work with my 2 kids to study during holidays.
Thank you for your comment! I appreciate the feedback. No worries about your English, you have made yourself quite understandable and clear! I am glad you found the Modern Algebra Book 1! I guarantee you your children will notice the difference immediately compared to the rubbish in public schools today! Are you in the US?
7:13 "I want to work harder and harder. I believe I am here to work." That is the kind of mindset I admire. My deepest respect! When I hear something like that from a middle aged professor, who put 1000x more down to the table than me as a 24 year old student, then I always go silent. What a man! Many think it gives someone motivation or power to do more or work harder. For me not. For me, such a strong statement puts me in shame. That is what I feel. But that is good. The shame itself motivates me to work harder because if that professor can, so can I. I must! There is no way I can not. Mr. Cromwell, what I see, that along your mathematical journey there was not a particular state you have said yourself "I stop here". Many will do this I guess. But only the very best ones learn till death. Simply magnificent!!!!
Thank you! I'm just too stubborn to stop, and the universe keeps humoring me with more math to ponder. As for learning till death, I think it’s about being endlessly curious! Many people today squander away their money (the little they have!) on useless junk made in China...to get a temporary dopamine hit...but for me, Math is my dopamine and it sure is a lot cheaper (and more beneficial) than all that expensive rubbish bought on credit that so many people buy! Keep that fire alive, my friend-shame is a fine motivator, but passion for truth lasts longer!
I remember a similar quiz in your class and I definitely failed but then I remember you gave us amazing notes...but yeah the guys who were from public school really had a hard time in your class but all for the better.
Could you clarify what you mean by 'theoretical underpinnings'? Are you asking about the foundational theories I rely on, or how I explain the significance of my work in a broader mathematical context?
In the US, we do NOT have a national curriculum, so the closest thing that comes to that is the "common core". However, the most typical Algebra 2 topics are as follows in public schools (here at City Tutoring we go way deeper and maintain the old school curriculum, but I am giving you what most public school students in the US would likely cover, in no particular order): Order of Operations, Solving Linear Equations, Writing Linear Equations(slope, slope-intercept form, point-slope form), Graphing Linear Equations, Absolute Value Equations, Solving Linear Inequalities(including compound inequalities) Absolute Value Inequalities, Graphing Absolute Value Functions (Parent Function & Transformations), Graphing Quadratic Functions (Parent Function & Transformations) Characteristics of Functions (Linear, Abs. Value & Quadratic), Domain/Range Increasing/Decreasing, End behavior, Min/Max, Factoring, GCF, Difference of Squares Trinomials with leading coefficient of 1, Trinomials with leading coefficient not equal to 1, Sum & Difference of Cubes, Solving Quadratics Solving Quadratics by Factoring Solving Quadratics by Graphing, Simplifying Radicals (prerequisite for quad formula, simplifying complex #s), Complex Numbers, Solving Quadratics by Quadratic Formula, Solving Quadratics by Completing the Square****Honors only!!! (this should be STANDARD but in many schools, they only include it in honors!) Polynomials, Exponential & Logarithmic Functions, Functions, Trigonometry (ideally), Radicals, Arithmetic and Geometric Sequences, Variation. This may vary a lot though depending on where you are in the US, but would be "typical".
@@citytutoring Thank you for the in-depth answer. I thought it important to clarify this in order to know what to reasonably expect from an Algebra 2 student.
Can you please elaborate on that if you can? If you were to get questions like the ones I show in the video, would you know how to tackle them or do you mean you have never seen the use of the discriminant? I am concerned. If they have not taught you that, shame on them!
@@citytutoring I can say I ran into a similar issue where my teacher in highschool was content with having us plug the right coefficients into the formula without ever mentioning the word "discriminant". When you then move on to the college-level the teachers all expect you to know how it works. Mostly because they were taught when they were in highschool.
@@citytutoring fortunately, when I took high school Algebra 2 in the early 2000s, we covered the discriminant, I believe. As a side note: I prefer to write the quadratic formula (do you abbreviate it as QF or Q.F.?) as follows: using (b)^2 + (-4 * a * c). So notice that I used parentheses and used addition. I feel this helps prevent mistakes.
I have seen three of your videos now, this one, "DID YOU FAIL THIS ALGEBRA II QUIZ? YOU NEED HELP!", and ""HONORS" ALGEBRA STUDENT FAILS A BASIC ALGEBRA TEST" and in each one there has been at least one critical mistake in either your writing of questions, language, or answers to questions. I just dont see how you can let such things slide as mixing up root 5 for being just 5 (16:55), among others from the aforementioned videos. You seem to have deep personal motivation to provide a better education for the american public, yet the resources you provide on youtube, and apparently to your own students as the tests have substantial errors in how they are formatted. I just dont understand how these issues so frequently arise and believe that the quality control for your tests and channel needs to be improved upon.,
Sir/Ma'am: Thank you for your comment about the materials/channel. I do take this very seriously, and appreciate your concern about the materials. We will continue to improve in that regard. A lot of the "critical" (I would not go so far as to put it that way) mistakes you mention are the result of typos or editing, due to the fact that I do not really have a lot of technology. I am very much off grid except that now I do my best to upload on TH-cam. In fact, I always mention that I do not even have any Computer Science background at all. Of course, that is not an excuse for not editing as best I can, but it does somewhat explain the gap between "in person", where I have no problems, and what you are noticing. Needless to say, I agree with you that striving for quality control is always a good thing. Thank you!
@@citytutoring ah, i understand how these errors may come about now thank you for clarifying. If i may ask, why are you essentially off grid? Also, I would like to mention that your work to fight against grade inflation and the flaws of the american education system as a whole is a noble and respectable pursuit that you seem to do quite well on the scale you have access to.
@@zegaz_5831 You're welcome! I am off grid, mostly, because of a series of lifestyle choices forged on from earlier ages where I believe, first and foremost, in self-sufficiency. My ancestors were all self-reliant settlers in America, so I am a firm believer in going my own way, with the help of God of course. Being off grid allows me to focus a lot on my work and my thoughts. Living off grid also helps me to be self-sufficient, so everything on my homestead is very much functional without the need for electricity, for example. My office/study is electrified, so that I can upload videos on here and respond, record videos, but other than these tasks, I find it very peaceful to be off the grid. I don't even have a mobile phone, because it is too distracting. I appreciate your kind comments, and I promise to you and to God to do my best in my next videos to avoid those editing mistakes. Please keep me accountable, because I appreciate people like you who take me to task! May you have a lovely evening, Alfred Cromwell.
Why is the world in such a mess, but you have all the top universities like harvard Yale and Princeton Oxford Cambridge.there is untold suffering in the world starvation crime etc.
Why do you say that? I fundamentally disagree. Of course, it will depend on what Enlightenment we are talking about, as there is a difference between the "French" version and the Scottish Enlightenment, for example, which was about freedom and enterprise, all compatible with the Christian faith. You could not have Western civilization without the acknowledgment of faith, reason, and philosophy, or, to put it simply, reason and religion, specifically, the Christian religion. That mix of Athenian concepts of government on the one hand, and Jerusalem on the other, have provided our historical spiritual foundation on which to defend freedom and rightly understood progress. So when I mention the Enlightenment, I am referring to the ideals of the American founders, which, although not all of them were Christian, the majority were most certainly influenced by Christianity, in a broad sense. Many were deists, but others were staunch Christians. One does not cancel out the other. In fact, I'd argue that freedom and our constitutional form of government complements Christian values. To quote former President Ronald Reagan, "a shining city on a hill".
thanks for your hard work. I love the rigourism that you enforce in your videos. I am working on my english, thanks again. I engage my kids to study mathematics with me, I just found the Modern Algebra book 1 that you showed the other day to work with my 2 kids to study during holidays.
Thank you for your comment! I appreciate the feedback. No worries about your English, you have made yourself quite understandable and clear! I am glad you found the Modern Algebra Book 1! I guarantee you your children will notice the difference immediately compared to the rubbish in public schools today! Are you in the US?
Rigourism? Rigor!
7:13 "I want to work harder and harder. I believe I am here to work." That is the kind of mindset I admire. My deepest respect! When I hear something like that from a middle aged professor, who put 1000x more down to the table than me as a 24 year old student, then I always go silent. What a man! Many think it gives someone motivation or power to do more or work harder. For me not. For me, such a strong statement puts me in shame. That is what I feel. But that is good. The shame itself motivates me to work harder because if that professor can, so can I. I must! There is no way I can not. Mr. Cromwell, what I see, that along your mathematical journey there was not a particular state you have said yourself "I stop here". Many will do this I guess. But only the very best ones learn till death. Simply magnificent!!!!
Thank you! I'm just too stubborn to stop, and the universe keeps humoring me with more math to ponder. As for learning till death, I think it’s about being endlessly curious! Many people today squander away their money (the little they have!) on useless junk made in China...to get a temporary dopamine hit...but for me, Math is my dopamine and it sure is a lot cheaper (and more beneficial) than all that expensive rubbish bought on credit that so many people buy!
Keep that fire alive, my friend-shame is a fine motivator, but passion for truth lasts longer!
@@citytutoring The last sentence hit me! Thank you!
I remember a similar quiz in your class and I definitely failed but then I remember you gave us amazing notes...but yeah the guys who were from public school really had a hard time in your class but all for the better.
We do Pure Maths here, not games. I'm glad it was beneficial to you! That's what I want to see!
Have you spoken of the theoretical underpinnings of the work you perform or specialise in within the math field?
Could you clarify what you mean by 'theoretical underpinnings'? Are you asking about the foundational theories I rely on, or how I explain the significance of my work in a broader mathematical context?
What are the topics typically covered in Algebra 2? Asking as a non-US resident
In the US, we do NOT have a national curriculum, so the closest thing that comes to that is the "common core". However, the most typical Algebra 2 topics are as follows in public schools (here at City Tutoring we go way deeper and maintain the old school curriculum, but I am giving you what most public school students in the US would likely cover, in no particular order):
Order of Operations, Solving Linear Equations, Writing Linear Equations(slope, slope-intercept form, point-slope form), Graphing Linear Equations, Absolute Value Equations, Solving Linear Inequalities(including compound inequalities)
Absolute Value Inequalities, Graphing Absolute Value Functions (Parent Function & Transformations), Graphing Quadratic Functions (Parent Function & Transformations)
Characteristics of Functions (Linear, Abs. Value & Quadratic), Domain/Range
Increasing/Decreasing, End behavior, Min/Max, Factoring, GCF, Difference of Squares
Trinomials with leading coefficient of 1, Trinomials with leading coefficient not equal to 1, Sum & Difference of Cubes, Solving Quadratics Solving Quadratics by Factoring Solving Quadratics by Graphing, Simplifying Radicals (prerequisite for quad formula, simplifying complex #s), Complex Numbers, Solving Quadratics by Quadratic Formula, Solving Quadratics by Completing the Square****Honors only!!! (this should be STANDARD but in many schools, they only include it in honors!)
Polynomials, Exponential & Logarithmic Functions, Functions, Trigonometry (ideally), Radicals, Arithmetic and Geometric Sequences, Variation.
This may vary a lot though depending on where you are in the US, but would be "typical".
@@citytutoring Thank you for the in-depth answer. I thought it important to clarify this in order to know what to reasonably expect from an Algebra 2 student.
Favorite complex analysis textbook?
I find that classics like 'Complex Analysis' by Lars Ahlfors are hard to beat. It's rigorous, elegant, and has stood the test of time.
I am perplexed as to why both Precalculus community college courses I've taken do not teach us to use the discriminant...
Can you please elaborate on that if you can? If you were to get questions like the ones I show in the video, would you know how to tackle them or do you mean you have never seen the use of the discriminant? I am concerned. If they have not taught you that, shame on them!
@@citytutoring I can say I ran into a similar issue where my teacher in highschool was content with having us plug the right coefficients into the formula without ever mentioning the word "discriminant". When you then move on to the college-level the teachers all expect you to know how it works. Mostly because they were taught when they were in highschool.
No wonder so many students are having so much difficulty in college mathematics. I see a decline in standards year after year.
@@citytutoring fortunately, when I took high school Algebra 2 in the early 2000s, we covered the discriminant, I believe.
As a side note: I prefer to write the quadratic formula (do you abbreviate it as QF or Q.F.?) as follows: using (b)^2 + (-4 * a * c).
So notice that I used parentheses and used addition. I feel this helps prevent mistakes.
@@citytutoring The trouble is that, as long as you get good grades, you don't really have a reason to question what's going on in your class.
I have seen three of your videos now, this one, "DID YOU FAIL THIS ALGEBRA II QUIZ? YOU NEED HELP!", and ""HONORS" ALGEBRA STUDENT FAILS A BASIC ALGEBRA TEST" and in each one there has been at least one critical mistake in either your writing of questions, language, or answers to questions. I just dont see how you can let such things slide as mixing up root 5 for being just 5 (16:55), among others from the aforementioned videos. You seem to have deep personal motivation to provide a better education for the american public, yet the resources you provide on youtube, and apparently to your own students as the tests have substantial errors in how they are formatted. I just dont understand how these issues so frequently arise and believe that the quality control for your tests and channel needs to be improved upon.,
Sir/Ma'am: Thank you for your comment about the materials/channel. I do take this very seriously, and appreciate your concern about the materials. We will continue to improve in that regard. A lot of the "critical" (I would not go so far as to put it that way) mistakes you mention are the result of typos or editing, due to the fact that I do not really have a lot of technology. I am very much off grid except that now I do my best to upload on TH-cam. In fact, I always mention that I do not even have any Computer Science background at all. Of course, that is not an excuse for not editing as best I can, but it does somewhat explain the gap between "in person", where I have no problems, and what you are noticing.
Needless to say, I agree with you that striving for quality control is always a good thing. Thank you!
@@citytutoring ah, i understand how these errors may come about now thank you for clarifying. If i may ask, why are you essentially off grid? Also, I would like to mention that your work to fight against grade inflation and the flaws of the american education system as a whole is a noble and respectable pursuit that you seem to do quite well on the scale you have access to.
@@zegaz_5831 You're welcome! I am off grid, mostly, because of a series of lifestyle choices forged on from earlier ages where I believe, first and foremost, in self-sufficiency. My ancestors were all self-reliant settlers in America, so I am a firm believer in going my own way, with the help of God of course. Being off grid allows me to focus a lot on my work and my thoughts. Living off grid also helps me to be self-sufficient, so everything on my homestead is very much functional without the need for electricity, for example. My office/study is electrified, so that I can upload videos on here and respond, record videos, but other than these tasks, I find it very peaceful to be off the grid. I don't even have a mobile phone, because it is too distracting. I appreciate your kind comments, and I promise to you and to God to do my best in my next videos to avoid those editing mistakes. Please keep me accountable, because I appreciate people like you who take me to task! May you have a lovely evening, Alfred Cromwell.
Why is the world in such a mess, but you have all the top universities like harvard Yale and Princeton Oxford Cambridge.there is untold suffering in the world starvation crime etc.
"I believe in the enlightenment within a Christian framework" is an oxymoron.
Why do you say that? I fundamentally disagree. Of course, it will depend on what Enlightenment we are talking about, as there is a difference between the "French" version and the Scottish Enlightenment, for example, which was about freedom and enterprise, all compatible with the Christian faith.
You could not have Western civilization without the acknowledgment of faith, reason, and philosophy, or, to put it simply, reason and religion, specifically, the Christian religion. That mix of Athenian concepts of government on the one hand, and Jerusalem on the other, have provided our historical spiritual foundation on which to defend freedom and rightly understood progress. So when I mention the Enlightenment, I am referring to the ideals of the American founders, which, although not all of them were Christian, the majority were most certainly influenced by Christianity, in a broad sense. Many were deists, but others were staunch Christians. One does not cancel out the other. In fact, I'd argue that freedom and our constitutional form of government complements Christian values. To quote former President Ronald Reagan, "a shining city on a hill".