Welcome to one of Schoolhouse's first AP Lit series! In this series we will go over a set list of literary works to read together, study them, then write about them. To minimize our out-of-session reading time commitment and maximize engagement, each session is structured as follows: - 50 minutes taking turns reading out loud, - 10 minutes of silence for in-session note-taking - 30 minutes discussing Total: 1h30m per session We would also have other sessions dedicated to AP English Literature prep specifically, including sessions on how to read, take proper notes, and write for the exam. Once we finish a given novel/short story/play/poem, we would have a seperate session to write an essay in the form of an AP English Literature essay, which I would review and give feedback on. Sessions are three days a week: Tuesday, Thursday, and Sunday. List of works: Poetry 1. Paradise Lost by John Milton 2. The Love Song of J. Alfred Prufrock Short Stories 1. White Nights by Fyodor Dostoevsky 2. Heart of Darkness by Joseph Conrad Books 1. 1984 and Animal Farm by George Orwell 2. To Kill a Mockingbird by Harper Lee 3. Demons by Fyodor Dostoevsky 4. The Trial by Franz Kafka Plays 1. A Raisin in the Sun by Lorraine Hansbery After we go through these, we may add group suggestions.

This is a full course covering the AoPS curriculum for Calculus, that prepares thoroughly for the AP Calculus Exam (Calculus 1 and 2) as well as serves as an introduction to Real Analysis (a full-course on proof-based Calculus). Sessions are 1h30m three times a week + 1h on Thursdays Prerequisites: -Algebra 2 with trig (with previous proof-writing or AoPS course experience preferred but not required) This course will cover significantly more content than the standard AP Calculus class, placing greater emphasis on mathematical rigour through proofs and very challenging problems than on rote repetition and memorization. You will still benefit if you already have experience with Calculus because of its radically different emphasis from most Calculus courses. Syllabus: Unit 0 - Sets and Functions (Review) Unit I - Limits and Continuity Unit II - The Derivative Unit III - Applications of the Derivative Unit IV - Integration Unit V - Infinity Unit VI - Series Unit VII - Plane Curves Unit VIII - Differential Equations We will use the AoPS Calculus textbook, which I will provide for those unable to get it themselves. We will also supplement from various other sources. Note: Required reading of 10 pages of reading before each session + homework due for each unit (with feedback).

Sessions are weekly and last 1h10m. Review and practice key SAT Math concepts before your upcoming exam with the help of a 780 scorer. The sessions will be divided into each of these three components: - 🔍 Review: Refresh your memory and solidify your understanding of key math topics across all four domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. - 💡 Tips: Receive valuable tips on math concepts, effective use of [Desmos](https://www.desmos.com/calculator), and strategies to help you excel on the SAT. - ✏️ Practice: Complete difficult practice problems to build your endurance and improve your problem-solving skills for the SAT. - This series is designed for those who are currently scoring in the 600+ range and are looking to improve on some of the hardest math topics that appear on the SAT. All are certainly welcome to join! Just keep in mind that we’ll be working quickly through difficult level problems. - Credit to @Joe H for helping me organize the series

This is a full first course on proof-based linear algebra. Sessions are 1h30m daily except for Sunday, so the course is at an accelerated pace. Prerequisites: -Algebra 2 with trig (with Calculus preferred but not required) Syllabus: (UNIT I) Basic Vector Operations 1. Vector geometry in R^n 2. Planes in R^3 3. Span, subspaces, and dimension 4. Basis and orthogonality 5. Cross Products (UNIT II) Basic Vector Space Properties 2. Vector Spaces and Subspaces 3. Linear independence and Gram-Schmidt 4. Projections and Orthogonal Vector Decomposition (Unit III) Linear Transformations and Motivating Matrices 5. Linear Transformations, Properties, and Kernel 6. Matrix operations, special matrices, and matrix properties (Unit IV) Linear Systems 7. Determinants, Linear Systems, and Inverse Matrices 8. LU decomposition 9. Row, Column, and Null Space, Rank and Nullity (Unit V) Representing Linear Transformations as Matrices 10. Change of Basis and Matrix Multiplication 11. Eigenvectors and Diagonalizability (Unit VI) Special Topics in Applied Linear Algebra: -Euclidean Inner Spaces -Least squares regression -Markov chains -Raising numbers to matrices -Solving differential equations using matrices I will provide all reading and practice material. Note: Required reading of 25 pages a week + Weekly homework (with feedback) + 1 test per unit (with review in-class and the tests graded with feedback).

Are you interested in learning Calculus 3? Well, this course is the equivalent of a second-semester course, a continuation of my last series. Don't worry though if you weren't there. This series can be taken by anyone who has completed the only prerequisite: Calculus 1 (with integration) and the rest of the necessary background information will be covered or reviewed in the initial sessions. NOTE: Required reading of about 35 pages a week (for units 2 and 3 only)+ weekly homework (with feedback) + 1 test per unit (inside or outside of class depending on time but always graded with feedback within 2 days) Sessions are between 1h15m to 1h30m. Content Covered: (UNIT I) Single-Variable Integration and Vector Analysis 1. Physical interpretations of the integral and the average value of a function over an interval 2. Finding the area between curves expressed as functions of y 3. Finding the area between curves that intersect at more than two points 4. Volumes with cross sections: squares, rectangles, triangles, and semicircles 5. Volume with the disc and washer method: revolving around x-, y-, and different axes 6. Arc length, distance traveled, and unit calculator practice 7. Defining and differentiating parametric vector-valued functions 8. Finding arc lengths of curves given by parametric equations and solving motion problems 9. Defining polar coordinates and differentiating in polar form 10. Finding the area of a polar region bounded by one and multiple polar curves, and unit calculator practice. 11. Finding the surface area of surfaces or revolution, including in polar coordinates. (UNIT II) Multivariable Integration and Applications 11. Formulating Riemann sums 12. The Double Integral and Iterated Integral 13. Applications of The Double Integral 14. Triple Integrals 15. The Jacobian and uv-substitution 16. Integration in Polar, Cylindrical, and Spherical Coordinates 17. Applications of Triple Integrals (Unit III) Multivariable Vector Analysis 18. Scalar-valued Line Integrals 19. Vector-valued line integrals 20. Path Independence 21. Exact Differentials 22. Divergence and Green's Theorem 23 Curl, Stokes' Theorem, and parameterizing surfaces. 24. Flux and Divergence Theorem 25+ (applications to Electrodynamics and other special topics?)

I got a 5 on the AP Calculus BC exam, and you can too. Having previously taught Calculus 1 (the AB curriculum) and now seeing the staggering amount of demand for further maths, I've decided to host this intensive, yet comprehensive series on Calculus 2, including a FULL work-through of a real past exam. The first two sessions will serve as a review of differential calculus. Below are what we will cover: INTEGRATION AND APPLICATIONS (UNIT 1) 1. Introduction to accumulation of change 2. Left and right Riemann sums; over and under-approximation 3. Midpoint and trapezoidal sums 4. Definition of indefinite integral using as the limit of Riemann sums 5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals 6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation. 7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds. 8. The reverse power rule, u-substitution, and integration by parts 9. Antiderivatives of all the previously mentioned functions 10. Improper integrals 11. Finding the average value of a function on an interval 12. Connecting position, velocity, and acceleration functions using integrals 13. Using accumulation functions and definite integrals in applied contexts 14. Finding the area between curves expressed as functions of x 15. Finding the area between curves expressed as functions of y 16. Finding the area between curves that intersect at more than two points 17. Volumes with cross sections: squares and rectangles 18. Volumes with cross sections: triangles and semicircles 19. Volume with disc method: revolving around x- or y-axis 20. Volume with disc method: revolving around other axes 21. Volume with washer method: revolving around x- or y-axis 22. Volume with washer method: revolving around other axes 23. The arc length of a smooth, planar curve and distance traveled 24. Calculator-active practice DIFFERENTIAL EQUATIONS (UNIT 2): 1. Modeling situations with differential equations 2. Verifying solutions for differential equations 3. Sketching slope fields 4. Reasoning using slope fields 5. Approximating solutions using Euler’s method 6. Finding general solutions using separation of variables 7. Finding particular solutions using initial conditions and separation of variables 8. Exponential models with differential equations 9. Logistic models with differential equations PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS (UNIT 3): 1. Defining and differentiating parametric equations 2. Second derivatives of parametric equations 3. Finding arc lengths of curves given by parametric equations 4. Defining and differentiating vector-valued functions 5. Solving motion problems using parametric and vector-valued functions 6. Defining polar coordinates and differentiating in polar form 7. Finding the area of a polar region or the area bounded by a single polar curve 8. Finding the area of the region bounded by two polar curves 9. Calculator-active practice INFINITE SERIES (UNIT 4): 1. Defining convergent and divergent infinite series 2. Working with geometric series 3. The nth-term test for divergence 4. Integral test for convergence 5. Harmonic series and p-series 6. Comparison tests for convergence 7. Alternating series test for convergence 8. Ratio test for convergence 9. Determining absolute or conditional convergence 10. Alternating series error bound 11. Finding Taylor polynomial approximations of functions 12. Lagrange error bound 13. Radius and interval of convergence of power series 14. Finding Taylor or Maclaurin series for a function 15. Representing functions as power series

Hey everyone, it's finally here! Calculus 3 (the equivalent of the first semester of a full-year course). NOTE: REQUIRED READING OF APPROXIMATELY 25 PAGES A WEEK + WEEKLY HOMEWORK (with feedback) + 1 TEST PER UNIT (in-class and graded with feedback) Prerequisites: - Calculus 1 and 2 (the equivalent of Calc BC) CONTENT COVERED: (UNIT I) Basic Vector Operation 1. Vector geometry in R^n 2. Planes in R^3 3. Span, subspaces, and dimension 4. Basis and orthogonality 5. Cross Products (UNIT II) Partial Derivatives and Applications 6. Multivariable functions, level sets, and contour plots 7. Partial derivatives and contour plots 8. Maxima, minima, and critical points 9. Gradients, local approximations, and gradient descent 10. Constrained optimization via Lagrange multipliers (UNIT III) Basic Matrix Operations 11. Linear functions, matrices, and the derivative matrix 12. Linear transformations and matrix multiplication 13. Matrix algebra 14. Multivariable Chain Rule 15. Matrix inverses and multivariable Newton’s method for zeros (UNIT IV) Further Matrix Properties 16. Linear independence and the Gram–Schmidt process 17. Matrix transpose, quadratic forms, and orthogonal matrices 18. Linear systems, column space, and null space 19. Matrix decompositions: QR-decomposition and LU-decomposition (UNIT V) Motivating the Second Derivative Test 20. Eigenvalues and eigenvectors 21. Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers 22. The Hessian and quadratic approximation 23. Application of the Hessian to local extrema

Hey everyone, it's finally here! Calculus 3 (the equivalent of the first semester of a full-year course). NOTE: REQUIRED READING OF APPROXIMATELY 45 PAGES A WEEK + WEEKLY HOMEWORK (graded with feedback) + 1 TEST PER UNIT (in-class and graded with feedback) Prerequisites: - Calculus 1 and 2 (the equivalent of Calc BC) CONTENT COVERED: (UNIT I) Geometry of vectors and projections 1. Vector geometry in R^n and correlation coefficients 2. Planes in R^3 3. Span, subspaces, and dimension 4. Basis and orthogonality 5. Projections 6. Applications of projections in R^n: orthogonal bases of planes (UNIT II) Multivariable functions and optimization 7. Multivariable functions, level sets, and contour plots 8. Partial derivatives and contour plots 9. Maxima, minima, and critical points 10. Gradients, local approximations, and gradient descent 11. Constrained optimization via Lagrange multipliers (UNIT III) Geometry and algebra of matrices 12. Linear functions, matrices, and the derivative matrix 13. Linear transformations and matrix multiplication 14. Matrix algebra 15. Multivariable Chain Rule 16. Matrix inverses and multivariable Newton’s method for zeros (UNIT IV) Further matrix algebra and linear systems 17. Linear independence and the Gram–Schmidt process 18. Matrix transpose, quadratic forms, and orthogonal matrices 19. Linear systems, column space, and null space 20. Matrix decompositions: QR-decomposition and LU-decomposition (UNIT V) Eigenvalues and second partial derivatives 21. Eigenvalues and eigenvectors 22. Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers 23. The Hessian and quadratic approximation 24. Grand finale: application of the Hessian to local extrema, and bon voyage

Hi everyone, I'm back! Having previously taught Calculus 1 (the AB curriculum) and now seeing the staggering amount of demand for further maths, I've decided to host this intensive, yet comprehensive series on Calculus 2 (the equivalent of the post-AB portion of AP Calculus BC) including a FULL work-through of a real past exam. The first two sessions will serve as a review of differential calculus. Below are what we will cover: INTEGRATION AND APPLICATIONS (UNIT 1) 1. Introduction to accumulation of change 2. Left and right Riemann sums; over and under-approximation 3. Midpoint and trapezoidal sums 4. Definition of indefinite integral using as the limit of Riemann sums 5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals 6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation. 7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds. 8. The reverse power rule, u-substitution, and integration by parts 9. Antiderivatives of all the previously mentioned functions 10. Improper integrals 11. Finding the average value of a function on an interval 12. Connecting position, velocity, and acceleration functions using integrals 13. Using accumulation functions and definite integrals in applied contexts 14. Finding the area between curves expressed as functions of x 15. Finding the area between curves expressed as functions of y 16. Finding the area between curves that intersect at more than two points 17. Volumes with cross sections: squares and rectangles 18. Volumes with cross sections: triangles and semicircles 19. Volume with disc method: revolving around x- or y-axis 20. Volume with disc method: revolving around other axes 21. Volume with washer method: revolving around x- or y-axis 22. Volume with washer method: revolving around other axes 23. The arc length of a smooth, planar curve and distance traveled 24. Calculator-active practice DIFFERENTIAL EQUATIONS (UNIT 2): 1. Modeling situations with differential equations 2. Verifying solutions for differential equations 3. Sketching slope fields 4. Reasoning using slope fields 5. Approximating solutions using Euler’s method 6. Finding general solutions using separation of variables 7. Finding particular solutions using initial conditions and separation of variables 8. Exponential models with differential equations 9. Logistic models with differential equations PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS (UNIT 3): 1. Defining and differentiating parametric equations 2. Second derivatives of parametric equations 3. Finding arc lengths of curves given by parametric equations 4. Defining and differentiating vector-valued functions 5. Solving motion problems using parametric and vector-valued functions 6. Defining polar coordinates and differentiating in polar form 7. Finding the area of a polar region or the area bounded by a single polar curve 8. Finding the area of the region bounded by two polar curves 9. Calculator-active practice INFINITE SERIES (UNIT 4): 1. Defining convergent and divergent infinite series 2. Working with geometric series 3. The nth-term test for divergence 4. Integral test for convergence 5. Harmonic series and p-series 6. Comparison tests for convergence 7. Alternating series test for convergence 8. Ratio test for convergence 9. Determining absolute or conditional convergence 10. Alternating series error bound 11. Finding Taylor polynomial approximations of functions 12. Lagrange error bound 13. Radius and interval of convergence of power series 14. Finding Taylor or Maclaurin series for a function 15. Representing functions as power series

Hey everyone! We’re excited to welcome you to the committee sessions for the (committee name) committee of the Schoolhouse Model United Nations 2024! Schoolhouse MUN is an online Model United Nations event organised by a team of schoolhouse.world volunteers in which delegates will get the chance to represent different countries in 6 different committees of the United Nations to gain exposure to how the UN works, enhancing their knowledge on current world issues and improving their public speaking, collaboration and leadership skills. The UNDP committee will be chaired by Kirill and Alexander. The agenda for our committee is: accelerating the creation of inclusive and sustainable industrial development. If you haven’t already, register for the main event’s series here: https://schoolhouse.world/series/12576 Please note that you need to join at least three committee sessions to receive a certificate of participation. If you’re unsure of your committee allocation, please take a look at the event coda doc. If you’d like to join as an audience member, we’d love to have you there! We look forward to seeing you at the committee sessions!

Hey everyone! We are really excited to welcome you all to the second edition of the Schoolhouse Model United Nations! What is an MUN and Why Should You Participate? For those who may not be familiar with MUN, it stands for Model United Nations, which is a simulation of the United Nations, with delegates taking on the role of a country’s representative to discuss and find solutions to pressing global issues. MUNs are a great opportunity to develop your public speaking, negotiation and problem-solving skills. And we’re excited to host the second edition of Schoolhouse MUN to give y’all these opportunities on the Schoolhouse.world platform! About the Event: The event will consist of opening and closing ceremonies, with training sessions for all delegates. There are six committees, with the details for each as follows: United Nations Development Programme: Accelerating the creation of inclusive and sustainable industrial development United Nations General Assembly: Discussing causes and solutions to animal extinction United Nations Environment Programme: Analysing the progress of the Paris Climate Agreement United Nations Educational, Scientific and Cultural Organisation: Discussing the viability of a Common Universal Education System United Nations Women: Economic and political empowerment of women Food and Agricultural Organisation: Assessing the causes and consequences of unequal food distribution across landmasses and regions The event will take place from 13th to 14th January, 2024 (Eastern Hemisphere time), with 3 committee sessions taking place everyday, each for one hour. Each delegate who attends at least half of the committee sessions will receive a participation certificate, and winners will receive certificates of excellence. The best delegates from each committee will also win Schoolhouse merchandise! How to Participate: 1. Register for this series to be a part of the opening and closing ceremonies, as well as the training sessions for all delegates. 2. Fill in the committee preference form so that you will be allotted your committee and portfolio: [https://forms.gle/KEq1UMEzisAw9nYs9](https://forms.gle/KEq1UMEzisAw9nYs9) 3. Your committee and portfolio will be assigned to you, and study materials for the same will be shared. After that, you’ll have to register for your committee’s series. The link for the same will be shared with you. 4. Read the rules of procedure and the study material thoroughly, and research further on your committee’s agenda and your country’s stance regarding it to prepare for the conference. 5. Take part in the conference! For further details about the event, please take a look at the official event coda doc: [https://coda.io/@hafsahm/schoolhouse-model-united-nations-2024](https://coda.io/@hafsahm/schoolhouse-model-united-nations-2024) [](https://coda.io/@hafsahm/schoolhouse-model-united-nations-2024) If you have any questions, feel free to ask them in the series public discussion below or reach out to [email protected], and we’d be happy to answer! Note: If you’d like to join the event as an audience member, you are more than welcome to do so! We hope you will join us for this exciting and enriching opportunity to learn about global issues and hone your public speaking and negotiation skills. We look forward to seeing you there!

(Reboot of my last series) Hi, everyone! I'm proud to present Schoolhouse's first series on Linear Algebra! In this class we will cover all the standard topics of a first class in Linear Algebra (typically take sometime after Calc 2 for greater mathematical maturity, though it can be taken after Calc 3 or before Calculus in the first place.) To be clear, here are the pre-requisites: Algebra (1 and 2, and including Trig) are mandatory. Calculus 1 and 2 are strongly recommended just for maturity, but not required (if you get straight A's in all of Algebra 2 and Trig you should mostly be fine); Calc 3 helps as well (and when I set up my Calc 3 series we will be employing Linear Algebra so if that interests you this course is recommended.) I've taken Multivariable Calculus with Linear Algebra (applied) as well as Linear Algebra itself (proof-based) at Stanford OHS and Stanford ULO, getting an average of B+ on both, and am currently finishing Real Analysis. Generally, here are the topics we will cover (each week): 1. Basic vector operations in R^n 2. Vector Spaces and Subspaces induction technique. 3. Linear independence and Gram-Schmidt 4. Projections and Fourier's Formula 5. Linear Transformations, Properties, and Kernel 6. Matrix operations, special matrices, and matrix properties. 7. Determinants, Linear Systems, Inverse Matrices, and LU decomposition 8. Row, Column, and Null Space, Rank and Nullity 9. Change of Basis, Eigeneverything, and Diagonalizability 10. TBD: QR Decomposition and more on Transpose, Orthogonal Complements, Markov Chains, or anything else. The course expectation is at least 5 hours per week apart from class, office hours, and quizzes. (About 3 hours reading and 2 hours doing homework.) We will meet every Thursday and Saturday at the same time. In class we will not cover all the content (there is simply not enough time), rather we will discuss and go over the proofs the main results, which also appear in the text. We will skip over proofs and results whose proofs we all understand. We will focus on examples and practice in preparation for the assigned exercises and quizzes. We will use Bronson's "Linear Algebra - Algorithms, Applications, and Techniques" as our main text, ([http://ndl.ethernet.edu.et/bitstream/123456789/24629/1/Richard%20Bronson.pdf](http://ndl.ethernet.edu.et/bitstream/123456789/24629/1/Richard%20Bronson.pdf) ) in addition to Stanford's Math 51 text (fragments taken under fair use law which will be posted gradually).

Hi, everyone! I'm proud to present Schoolhouse's first series on Linear Algebra! In this class we will cover all the standard topics of a first class in Linear Algebra (typically take sometime after Calc 2 for greater mathematical maturity, though it can be taken after Calc 3 or before Calculus in the first place.) To be clear, here are the pre-requisites: Algebra (1 and 2, and including Trig) are mandatory. Calculus 1 and 2 are strongly recommended just for maturity, but not required (if you get straight A's in all of Algebra 2 and Trig you should mostly be fine); Calc 3 helps as well (and when I set up my Calc 3 series we will be employing Linear Algebra so if that interests you this course is recommended.) I've taken Multivariable Calculus with Linear Algebra (applied) as well as Linear Algebra itself (proof-based) at Stanford OHS and Stanford ULO, getting an average of B+ on both. Generally, here are the topics we will cover (each week): 1. Basic vector operations in R^n 2. Vector Spaces and Subspaces induction technique. 3. Linear independence and Gram-Schmidt 4. Projections and Fourier's Formula 5. Linear Transformations, Properties, and Kernel 6. Matrix operations, special matrices, and matrix properties. 7. Determinants, Linear Systems, Inverse Matrices, and LU decomposition 8. Row, Column, and Null Space, Rank and Nullity 9. Change of Basis, Eigeneverything, and Diagonalizability 10. TBD: QR Decomposition and more on Transpose, Orthogonal Complements, Markov Chains, or anything else. The course expectation is at least 5 hours per week apart from class, office hours, and quizzes. (About 3 hours reading and 2 hours doing homework.) We will meet every Saturday at the same time. In class we will not cover all the content (there is simply enough time), rather we will discuss and go over the proofs the main results, which also appear in the text. We will skip over proofs and results whose proofs we all understand. We will focus on examples and practice in preparation for the assigned exercises and quizzes. We will use Bronson's "Linear Algebra - Algorithms, Applications, and Techniques" as our main text, ( http://ndl.ethernet.edu.et/bitstream/123456789/24629/1/Richard%20Bronson.pdf ) in addition to Stanford's Math 51 text (fragments taken under fair use law which will be posted gradually).

Finally! The long-awaited series in Calculus is here. Main resources being used: AoPS and Khan Academy Pre-requisites: Trigonometry, Algebra 1, Algebra 2, and Precalculus (recommended but not required). The session descriptions are posted below, so please check them out! This is the first of three series I will be hosting, covering Calculus 1, 2, and 3. After each series ends I will host the next. In this course we will be covering the following: LIMITS AND CONTINUITY (Unit 1) - Introduction to limits - One and two-sided limits - Creating tables to approximate limits; approximating limits using tables - Limits of composite functions - Evaluating limits through direct substitution -Limits of trigonometric and piecewise functions -Evaluating limits by rationalizing and by using trigonometric identities -Squeeze theorem and applications -Introduction to continuity and types of discontinuities -Continuity at a point and over an interval -Removing discontinuities -Limits at infinity and limits at infinity of quotients -The Intermediate Value Theorem -The formal epsilon-delta definition of a limit DERIVATIVES (Unit 2): -Introduction to derivatives and notation -Average rate of change and the secant line -Instantaneous rate of change and the tangent line -The formal and informal definition of a derivative using limits -Equation of the tangent line of a function at a point -Estimating derivatives graphically and algebraically -Differentiability at a point and over an interval (connection to continuity) -Evaluating derivatives using the power rule, sum rule, product rule, quotient rule, and chain rule (including proofs of all the rules) -Derivative of sin(x), cos(x), tan(x), csc(x), sec(x), cot(x), ln(x), e^x, a^x, and log_a(x) (including a derivation of all of the formulas) -Derivative of inverse functions and inverse trigonometric functions -Second derivatives, implicit differentiation, and related rates -Position, velocity, and acceleration problems -Local linearity and linear approximations to functions -L'Hôpital's rule and the special case of L'Hôpital's rule -The Mean Value Theorem for derivatives, the Extreme Value Theorem, and Rolle's Theorem -Finding critical points, local minima and maxima, increasing and decreasing intervals of a function -Finding absolute extrema over closed intervals and over the entire domain of a function -Introduction to concavity -The Second Derivative Test and points of inflection -Optimization INTRODUCTION TO INTEGRATION (Unit 3) -introduction to accumulation of change -Left and right Riemann sums; over and under-approximation -Midpoint and trapezoidal sums -Definition of indefinite integral using as the limit of Riemann sums -The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals -Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation. -Integrating sums of functions, switching the bounds of integration, and with functions as bounds. -The reverse power rule, u-substitution, and integration by parts -Antiderivatives of all the previously mentioned functions -Improper integrals

Hey guys! Along with my Geometry series, here's one for Algebra 2 and Trig! It's never too early/late to start learning, so why not join? Prerequisites: Algebra 1; good grasp of quadratics (which you can learn concurrently if you haven't already). We're going to be covering -Polynomials -Vectors -Complex Numbers -Rational Functions -Exponents/Logarithms -Function Transformations -Linear Transformations using Matrices -Types of triangles -Right Triangle Trigonometry -Unit Circle and Trigonometric Identities/Values -Radians and Degrees -Trigonometric Functions -Inverse Trigonometric Functions -Sinusoidal Graphs/Equations -Other Trigonometric Identities

Hey guys, I decided to make a new, comprehensive series on Geometry, including matrices, vectors, and other concepts to discuss planes, shapes in 3-dimensions, etc. IMPORTANT: You can join this series AFTER it has begun in case there are any specific topics you would like to learn or review! This series we will covering all Khan Academy Courses on Basic Geometry, High School Geometry, as well as an introduction to linear algebra. The units we'll be doing are the following: Geometry Foundations, Triangles, Area and Perimeter, Surface Area and Volume, Polygons, Performing Transformations, Transformation properties and proofs, Congruence, Similarity, Analytical Geometry, Conic Sections, Circles, and Solid Geometry, Vectors and Matrices, and Planes. This series is for students who have already completed Pre-algebra and Arithmetic and are eager to learn! Some units may require some knowledge of Algebra 1, but we will cover that as well in our sessions.

Book List: https://docs.google.com/document/d/1rqjpwv7Xn5WSZJJXzjFNq7QN-h-IvwwlyNrBZG9Z2SM/edit?usp=sharing Office Hours: https://schoolhouse.world/series/1639?celebrate The aim of this series is to analyze Capitalist and Socialist Theory from an objective point of view. We will read Adam Smith and Karl Marx, among many, many more. We will read their critics, discuss the ideas we read in our sessions, and (optionally) write essays analyzing, comparing, and contrasting their ideas. This series is the third part--on Socialism. How we structure each session will be based on this guide: http://www.greatbooks.org/wp-content/uploads/2014/12/Shared-Inquiry-Handbook.pdf Sessions will be added continually.

Book List: https://docs.google.com/document/d/1rqjpwv7Xn5WSZJJXzjFNq7QN-h-IvwwlyNrBZG9Z2SM/edit?usp=sharing Office Hours: https://schoolhouse.world/series/1639?celebrate The aim of this series is to analyze Capitalist and Socialist Theory from an objective point of view. We will read Adam Smith and Karl Marx, among many, many more. We will read their critics, discuss the ideas we read in our sessions, and (optionally) write essays analyzing, comparing, and contrasting their ideas. This series is just the second part--on the role of government (liberty v. equality). How we structure each session will be based on this guide: http://www.greatbooks.org/wp-content/uploads/2014/12/Shared-Inquiry-Handbook.pdf Sessions will be added continually.

Hey guys, wanna get ahead of the curve? Wanna catch-up or reinforce your skills? I'm hosting this series because I really enjoyed my Algebra 2 and Trigonometry series in the past and because of popular demand. In this series we'll cover: -Polynomials (polynomial arithmetic, factoring, remainder and factor theorem, solving equations, features of graphs) -Vectors -Complex Numbers and Equations -Rational Functions -Exponents/Logarithms (Arithmetic, Algebra, and Graphs) -Function Transformations -Types of triangles, - General Triangle Properties -Circumcenter, Centroid, Altitudes, and Medians -Triangular Pyramids and Prisms (and their brain bending properties :) -Right Triangle Trigonometry (SOHCAHTOA, Complementary Angles, Reciprocal Trigonometric Ratios, etc.) -Unit Circle and Trigonometric Identities/Values -Radians and Degrees -Trigonometric Functions -Inverse Trigonometric Functions -Sinusoidal Graphs/Equations -Other Trigonometric Identities

This is just an office hours session, hosted every Wednesday at 3:30pm CST.

Book List: https://docs.google.com/document/d/1rqjpwv7Xn5WSZJJXzjFNq7QN-h-IvwwlyNrBZG9Z2SM/edit?usp=sharing Office Hours: https://schoolhouse.world/series/1639?celebrate The aim of this series is to analyze Capitalist and Socialist Theory from an objective point of view. We will read Adam Smith and Karl Marx, among many, many more. We will read their critics, discuss the ideas we read in our sessions, and (optionally) write essays analyzing, comparing, and contrasting their ideas. This series is just the first part--on Capitalism. How we structure each session will be based on this guide: http://www.greatbooks.org/wp-content/uploads/2014/12/Shared-Inquiry-Handbook.pdf Sessions will be added continually.

Welcome! In this series we'll start with the very basics of triangles and end with advanced trigonometry! Are you ready? We'll cover: -Types of triangles, - General Triangle Properties -Circumcenter, Centroid, Altitudes, and Medians -Triangular Pyramids and Prisms (and their brain bending properties :) -Right Triangle Trigonometry (SOHCAHTOA, Complementary Angles, Reciprocal Trigonometric Ratios, etc.) -Unit Circle and Trigonometric Identities/Values -Radians and Degrees -Trigonometric Functions -Inverse Trigonometric Functions -Sinusoidal Graphs/Equations -Angle Addition Identities -(other) Trigonometric Identities Each session will be about an hour to an hour and a half and we'll end each session with a Quizziz (game). Catch-up sessions are always available, just ask! Everything is organized in a google sites (homework, resources, slides, etc.) Pre-requisite: Pre-Algebra; Algebra and Geometry in general are also useful and recommended, but not required. YOU CAN ALWAYS JOIN AFTER THE SERIES HAS BEGUN!

Hey guys! Along with my Pre-Algebra/Algebra 1 series, here's one for Algebra 2! It's never too early/late to start learning, so why not join? Prerequisites: Algebra 1 recommended, at least be learning Quadratics (if you haven't already). We're going to be covering -Polynomials (polynomial arithmetic, factoring, remainder and factor theorem, solving equations, features of graphs) -Vectors -Complex Numbers -Rational Functions -Exponents/Logarithms (Arithmetic, Algebra, and Graphs) -Function Transformations -Linear Transformations using Matrices -Modeling Each session is an hour to an hour and a half. We will have sessions each Tuesday and Thursday. At the end of each session we will test our knowledge with a Quizz. All of my sessions have slides that I share with learners, along with quizlets and related resources. Homework is optional but recommended and we go over it at the beginning of each session briefly. All of the resources (slides, homeworks, etc. is organized on a google sites which I share with everyone). YOU CAN JOIN AFTER THE SERIES HAS STARTED! This is going to be a lot of fun, are you ready?

Hey guys! After receiving a considerable number of requests to host an Algebra series after my recent Geometry w/Trig, I decided to do it! :) Once again, we're going to start from the very beginning of Algebra up to Algebra 1. By the end of the series you will be familiar with... - Single/Multi-varied equations and how to solve them - Rates, Percentages, and Ratios (as well as basic rational equations and how to solve them) -Linear Functions/systems of equations w/Inequalities -Functions (domain, codomain, range, inverse, composite, transformations) -Absolute and pice-wise equations - Exponentials (properties of and functions) -Factoring basic polynomials/quadratics -Forms of quadratics/solving quadratic equations -Complex Numbers -Sequences (arithmetic and geometric). Each session is an hour to an hour and a half. We will have sessions each Monday and Wedsnday. At the end of each session we will test our knowledge with a Quizz. All of my sessions have slides that I share with learners, along with quizlets and relate resources. Homework is optional but recommended and we go over it at the beginning of each session briefly. All of the resources (slides, homeworks, etc. is organized on a google sites which I share with everyone). You can always join even after the series has begun, I'm always open to hosting catch-up sessions :) YOU CAN JOIN THE SERIES AFTER IT'S BEGUN! This is going to be a lot of fun, are you ready?

Hey guys, Since there was much demand for my original series on high school geometry, I decided to make a new, comprehensive series on Geometry, from the very basics to advanced trigonometry. IMPORTANT: You can join this series AFTER it has begun in case there are any specific topics you would like to learn or review! As I said, in this series we will covering all Khan Academy Courses on Basic Geometry, High School Geometry, and Trigonometry. The units we'll be doing are the following: Geometry Foundations, Triangles, Area and Perimeter, Surface Area and Volume, Polygons, Performing Transformations, Transformation properties and proofs, Congruence, Similarity, Right angles and trigonometry, Advanced Trigonometry, Analytical Geometry, Conic Sections, Circles, and Solid Geometry. This series is for students who have already completed Prealgebra and Arithmetic and are eager to learn! This series is also intended for learners who learn better through conversation and discussion rather than idle videos.

Hi everyone! Welcome to this High School Geometry Series where we will learn to do the following: - Performing Transformations -Transformation properties and proofs - Congruence. - Similarity -Right angles and trigonometry. - Analytical Geometry - Conic Sections -Circles -Solid Geometry. I am also certified in Pre-Algebra and Algebra 1, and I am finishing up Algebra 2, so I am also able to explain relations between Algebra and Geometry. We will meet every Saturday and Sunday at 6:00pm. If anyone needs to join at another time, I am open to accommodating the schedule, so don't worry! This series is primarily intended for motivated students (in 8th to 10th grade) who want to either get ahead or review (for older students). Prerequisites: Arithmetic. This series is also intended for learners who learn better through conversation and discussion rather than idle videos. IMPORTANT: You can join this series AFTER it has begun in case there are any specific topics you would like to learn or review!