I’m studying to take an entrance exam, and I need to learn how to do a bunch of math. Decimals, fractions, division, algebra, multiplication and subtraction. I’ve done a lot of googling to find the best book for this, but can’t find a good one. Does anyone have any recommendations? Thanks in advance!

Discrete Mathematics and Its Applications Kenneth H. Rosen vs Discrete Mathematics with Applications by Susanna S. Epp

I'm between these two, I'm thinking of studying discrete mathematics and then algorithms, I did some research on both and I've seen that people describe them as "a dry read without much motivation to learn on your own if you don't have a teacher to help you".

My circumstances are these, I have to learn these topics* for my discrete mathematics class, but the materials they give at my school are of very poor quality.

Any recommendations would be very helpful. I mean, about the books above, I don't know which one is the easiest to digest, or if there is a better one, more well-known one that people use to learn this. It's not that I'm looking for something easy, but more than anything, something that can guarantee me to learn in the best way, but without being terribly complex.

*Logic and sets
Relations and recurrence relations
Computational complexity
Graph theory
Probability and counting

Hi r/mathbooks can you recommend me some good textbooks that will cover most of the topics suggested below?

I know this is really big list, but I hope someone will take a quick look into it and give some insights.

_____________________

Algebra

Permutations: Definition of permutations, parity of permutations. Product of permutations, decomposition of permutations into products of transpositions and independent cycles.

Complex Numbers: Geometric representation, algebraic and trigonometric forms of recording, extraction of roots, roots of unity.

Systems of Linear Equations: Triangular matrices. Reduction of matrices and systems of linear equations to step form. Gauss's method.

Linear Dependence and Rank: Linear dependence of rows/columns. Main lemma on linear dependence, basis, and rank of a system of rows/columns. Rank of a matrix. Criterion for the consistency and determinacy of a system of linear equations in terms of matrix ranks. Fundamental system of solutions of a homogeneous system of linear equations.

Determinants: Determinant of a square matrix, its main properties. Criterion for non-zero determinant. Formula for expanding determinants by row/column.

Matrix Operations and Properties: Theorem on the rank of a product of two matrices. Determinants of products of square matrices. Inverse matrix, its explicit form (formula), method of expression using elementary row transformations.

Vector Spaces: Basis. Vector space dimension, concept of dimension. Decomposition of coordinates in a vector space. Subspaces as sets of solutions of homogeneous linear equations. Relationship between the dimension of the sum and intersection of two subspaces. Linear independence in subspaces. Basis and dimension of the direct sum of subspaces.

Linear Mappings and Linear Operators: Linear mappings, their representation in coordinates. Image and kernel of a linear mapping, relation to dimension. Transition to a conjugate space and conjugate bases. Changing the matrix of a linear operator when transitioning to another basis.

Bilinear and Quadratic Functions: Bilinear functions, their representation in coordinates. Changing the matrix of a bilinear function when transitioning to another basis. Orthogonal complement to a subspace with respect to a symmetric bilinear function. Relationship between symmetric bilinear and quadratic functions. Symmetric bilinear function normal form. Positive-definite quadratic functions. Law of inertia.

Euclidean Space: Introduction of the Cauchy–Bunyakovsky–Schwarz inequality. Orthogonal bases. Gram-Schmidt orthogonalization. Orthogonal operators.

Eigenvalues and Eigenvectors of Linear Operators: Eigenvalues and eigenvectors of a linear operator. Invariant subspaces of a linear operator, their linear independence. Conditions for diagonalizability of an operator.

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Mathematical Analysis

Limits of Sequences and Their Properties: Intermediate value theorem for sequences. Weierstrass theorem on bounded monotonic sequences.

Limits of Functions at a Point and at Infinity, and Their Properties: Intermediate value theorem for functions. Cauchy's criterion for the existence of a finite limit of a function. Existence of one-sided limits and monotonic functions. First and second remarkable limits.

Continuity of a Function at a Point: Unilateral continuity. Properties of functions continuous on an interval: boundedness, attainment of minimum and maximum values, intermediate value theorem for continuous functions.

Big-O Notation and Asymptotic Estimates.

Derivative of a Function of One Variable: Unilateral derivative. Continuity of functions with a derivative. Differentiability of functions at a point. Mechanical and geometric meanings of derivative and differentiability. Properties of derivatives. Elementary derivatives. Higher-order derivatives.

Theorems of Rolle, Lagrange, and Cauchy: Finding local extrema, determining convexity and inflection points, studying functions using derivatives. Taylor's formula. L'Hôpital's Rule.

Functions of Multiple Variables, Their Continuity and Differentiability: Partial derivatives. Gradient and its geometric meaning. Directional derivative. Hessian. Method of gradient descent. Finding extrema of functions of multiple variables. Finding constrained extrema of functions of several variables, method of Lagrange multipliers. Implicit function theorem.

Integration: Definite and indefinite integrals, their connection. Methods of integrating functions. Primary antiderivatives of various elementary functions. Multiple integrals (double, triple), change of coordinates, connection with curvilinear integrals.

Elements of Functional Analysis: Normed spaces, metric spaces, completeness, boundedness.

Series, Numerical and Functional Series: Convergence criteria (D'Alembert, Cauchy, integral test, Leibniz). Absolute and conditional convergence of series. Abel and Dirichlet tests for convergence. Convergence of power series. Disk and radius of convergence. Cauchy-Hadamard formula for the radius of convergence.

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Basic Rules of Combinatorics: Rule for counting the number of combinatorial objects. Pigeonhole principle. Examples.

Sets: Euler circles, set operations. Inclusion-exclusion principle. Examples.

Combinations: Arrangements, permutations, and combinations. Binomial theorem. Pascal's triangle. Arrangements, permutations, and combinations with repetitions.

Graphs: Handshaking lemma. Graph connectivity. Trees and their properties. Eulerian and Hamiltonian graphs. Planar graphs, Euler's formula. Directed graphs, tournaments.

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Probability Theory

Basic Concepts of Probability Theory: Definition of a probability space, basic discrete cases (ordered and unordered samples, with or without replacement), classical probability model.

Conditional Probabilities: Definition of conditional probability, law of total probability, Bayes' formula. Independence of events in a probability space. Pairwise independence and mutual independence.

Random Variables as Measurable Functions: Distribution function. Density function. Independence of random variables. Random vectors.

Expectation in Discrete and Absolutely Continuous Cases, variance, covariance, and correlation. Their main properties. Variance of the sum of independent random variables. Expectation and covariance matrix of a random vector. Symmetry and positive semi-definiteness of the covariance matrix. General expectation of a random variable.

Distributions: Standard discrete and continuous distributions, their expectations, variances, and properties:

Binomial

Uniform

Normal and multivariate normal

Poisson

Exponential

Geometric

I'm giving away a collection of about 500 math and science books. Most are textbooks, and most textbooks are math textbooks, with physics coming in second, and a few chemistry, biology, and computer science books. There are also some pop-science books.

There some good stuff in there, like Spivak's Calculus, Needham's Visual Complex Analysis, Feynman Lectures on Physics, Griffiths Introduction to Electrodynamics, etc. I've attached photos of the bookshelves before the books were packed up.

The catch is that you have to pick them up in Seattle, Washington. They are packed in 21 small 1.5 cu. ft. moving boxes. No, I will not ship them to you, even if you offer pay for the shipping. And no, I will not pull out individual books from the collection, this is an all or nothing proposition.

If you are interested, send me a message, and include your location and when and how you are able to pick them up in Seattle.

"I was a student in preparatory classes and now I want to go back and work on the math curriculum at that level. I’ve found three good analysis books that cover the entire program and include hundreds of exercises. However, my concern is what branch of mathematics I should study afterward. I want to dedicate my life to math, but I'm worried that after putting in a lot of effort, I’ll encounter obstacles like a lack of resources, especially since I’m used to working with a lot of materials."

does anyone have a pdf file of this book 9th generationFundamentals of differential equations and boundary value problems, Nagle, Saff Snider

What books , research papers , academic journals can I read in mathematics as a highschooler . I have looked for lot of research papers in general but as of now I just lack the knowledge and skill set to understand it nicely . Is there any reading material out there which is easier for me to understand and develops my interest in mathematics even more . Something which is not that fancy and daunting but instead keeps me glued and introduces me to the beauty of mathematics ?

Hello, I'd like to start learning about Dynamical Systems but I'm not sure where to start. Any book recommendations would be helpful!

Have looked on amazon but it seems all options (at least the top listings) don’t have good explanations and/or have a lot of mistakes.

Any suggestions will be appreciated.

I know I am probably getting in way over my head and that this subject can be extremely challenging and boring at times, but I am seeking guidance on it. A book like this probably isn’t super common, so help is appreciated.

Hi everyone,

I’m pursuing a Master’s degree in Mathematics and coming from a physics background (undergrad in Italy). I’m now looking to dive deeper into measure theory, which I’ll need for future studies in analysis and probability. My professor has recommended a few textbooks for the course, but I won’t be able to attend the lectures regularly, so I need a resource that’s well-suited for self-study.

Here are the books my professor suggested:

•	L. Ambrosio, G. Da Prato, A. Mennucci: Introduction to Measure Theory and Integration
•	V.I. Bogachev: Measure Theory, Volume 1 (Springer-Verlag)
•	L.C. Evans, R.F. Gariepy: Measure Theory and Fine Properties of Functions (Revised Edition, Textbooks in Mathematics)
•	P.R. Halmos: Measure Theory
•	E.M. Stein, R. Shakarchi: Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis 3)

Since I’ll be studying on my own, I’m wondering which of these books is the best fit for self-learners, particularly with a physics background. I’m looking for something rigorous enough to deepen my understanding but also approachable without a lecturer guiding me.

Would love to hear your thoughts, especially if you’ve worked through any of these texts! Thanks!

For instance,

Lee's topological manifolds

Carothers Real Analysis

and Jones's measure theory

all have exercises integrated into the text, such that you do a bit of reading (maybe a page) and then there are exercises interspersed in the text. What are some other books that have this?

A textbook I've not personally read but highly commended by one of the professors at my university. Suitable for the advanced undergraduate or beginning graduate student in algebraic geometry. Near-perfect condition

Nicely written book that does not require commutative algebra as a prerequisite. For the moment it is available from the personal page of Dustin Ross, but the autors are looking for a publisher. Comparing to the books by Reid or by Smith and company this one is a truly introduction.

I intend to write my graduation thesis on Predicate Logic, which is part of the requirements for obtaining a Bachelor’s degree in Mathematics, specifically in predicate logic because I am very interested in this field. However, the extent of my knowledge is currently insufficient to write a solid thesis, so I need intermediate and advanced books to study more deeply, especially concerning the meaning of predicates and the relationship between the predicate and the subject. I understand this concept intuitively, but no specific definition of this predicative relationship comes to mind except that it is a function that maps variables to a set of true and false. Nevertheless, I wonder how this function can be defined precisely. I am also particularly interested in studying the algebra of predicate logic. The courses I have taken in logic are:

1. Logic and Set Theory I in college.
2. Logic and Set Theory II in college.
3. I am well-versed in the ZFC model.
4. I have knowledge of Aristotelian logic and have read several books on this topic.

Having trouble finding a decent curriculum/text book for geometry for a very advanced 8 year old. Books are either incredibly dense or absurdly juvenile (my son complained the most recent book I got him from Amazon was just full of colors and wackiness instead of of just spelling out a rule and giving him examples).

I already have the aops geometry book, this is my baseline I will use with him if I have too, we've already worked our way through their algebra book, but their books are obviously geared towards like an advanced 12 year old and definitely on the upper bounds of what we need. We made it work over the summer when we had a lot of free time but I'd like something a little less aggressively paced/less dense for learning during the school year after he's already spent all day at school.

Ideally I'm looking for a classic 70's-1980's high school text book that simply lays out whatever the lesson/concept is for that section then works through it and has examples and questions.

Again I like AOPS, I know about AOPS, I expect the default advice is just to use those books and I don't disagree with that but I've got a unique situation where my very advanced but very young kid would benefit from a textbook that was maybe geared towards a normal 15 year old, instead of an advanced learner if that makes any sense.

I'm currently searching for a book on differential equations. I've managed to narrow down the initial selection to two books: Differential Equations with Applications and Historical Notes, 2017 by George F. Simmons and Differential Equations and Their Applications: An Introduction to Applied Mathematics, 1993 by Martin Braun.

I'm simply a person looking for a more comprehensive coverage of the subject. If you have any experience with any of the two books, please tell me what you think of it. If you have a different recommendation, please drop it and explain why you think it's a good read. If you're someone with a good background in differential equations but are not familiar with the books and have some free time, you can easily acquire free copies online and review them.

The artofproblemsolving recommendation is their five books for this!

1. Intro to Algebra
2. Intro Counting & Probability
3. Intro Geometry
4. Intermediate Algebra
5. PreCalculus

Looking at their table of contents, many topics are revisited in the book series, you can see too much overlapped. They probably go deeper on the subjects they overlapped but is it really necessary? Seems more time consuming.

I noticed some other stuff like having polynomial addition/subtraction/multiplication in the first book (intro to algebra) and doing polynomial division in the forth book (intermediate algebra).

All those books together are like ~4000 pages (including excercises).

I also posted this in r/math and r/learnmath - don't know if this forum is the right one? :) ... Here goes:

I almost finished reading (and working on exercises) in the book "Elliptic Tales" by Avner Ash and Robert Gross and it was PERFECT for the amount of time, energy and existing knowledge I have to use! :) I really liked remembering my knowledge of complex numbers, groups and modular arithmetic and REALLY liked learning a lot of new stuff!!

In the Preface they write: "A certain amount of mathematical sophistication is needed to read this book. We believe that if you've had and enjoyed a college course in calculus or beyond, and if you are patient, you probably have enough of this elusive quality to enjoy any chapter of the book"(!)

I've started reading and working on their first book "Fearless Symmetry", which is also good, but a bit too basic for me, since I've taken a few college courses in math. And since I just read the Elliptic book, which is somewhat heavier.

CAN YOU PLEASE RECOMMEND ME BOOKS SIMILAR TO "ELLIPTIC TALES" IN "DIFFICULTY"? I need to be able to appreciate it without a teacher, other students, and with around a years worth of college courses of pre-existing (old dusty) knowledge. And while doing a fulltime job and raising a kid :).

Thanks a lot in advance!

I want to get something for my siblings to help them with this course. I found these three books, but I don't know which one would be best. These options are:

-Calculus Made Easy by Silvanus Thompson

-Calculus for the Practical Man by JD Thompson

or

-Essential Calculus Skills Practice Workbook with Full Solutions by Chris McMullen

I need a book on Boolean algebra and lattices. A book with examples and question and well done theory part.

Any book suggested? Thanks.