Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_Through_Guided_Discovery_(Bogart)/01%3A_What_is_Combinatorics/1.02%3A_Basic_Counting_PrinciplesIn this section, we explore the basic counting principles through a plethora of examples and exercises. One of our goals in these notes is to show how most counting problems can be recognized as count...In this section, we explore the basic counting principles through a plethora of examples and exercises. One of our goals in these notes is to show how most counting problems can be recognized as counting all or some of the elements of a set of standard mathematical objects. You may have noticed some standard mathematical words and phrases such as set, ordered pair, function, and so on creeping into the problems.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_Through_Guided_Discovery_(Bogart)/04%3A_Generating_Functions/4.02%3A_Generating_Functions_for_Integer_PartitionsIn the previous section (Section 4.1), we discussed how to visualize variables in a function using images as well as different methods to help us generate functions. In this section, we will explore h...In the previous section (Section 4.1), we discussed how to visualize variables in a function using images as well as different methods to help us generate functions. In this section, we will explore how to generate functions for the number of partitions of an integer into parts of different sizes.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/25%3A_The_Binomial_Theorem/25.01%3A_The_Binomial_Theorem(a+b)3=(a+b)⋅(a+b)⋅(a+b)=(a2+2ab+b2)⋅(a+b)=a3+2a2b+ab2+a2b+2ab2+b3=a3+3a2b+3ab2+b3 \[\begin{aligned} (a+b)^4 &...(a+b)3=(a+b)⋅(a+b)⋅(a+b)=(a2+2ab+b2)⋅(a+b)=a3+2a2b+ab2+a2b+2ab2+b3=a3+3a2b+3ab2+b3 (a+b)4=(a+b)⋅(a+b)⋅(a+b)⋅(a+b)=(a3+3a2b+3ab2+b3)⋅(a+b)=a4+3a3b+3a2b2+ab3+a3b+3a2b2+3ab3+b4=a4+4a3b+6a2b2+4ab3+b4
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/01%3A_Introduction_and_Notation/1.04%3A_Definitions_of_Elementary_Number_TheoryIn this section, we discuss some basic definitions of terms related to the elementary number theory, including even and odd, decimal and Base-n notation, divisibility, floor and ceilings, div and mod,...In this section, we discuss some basic definitions of terms related to the elementary number theory, including even and odd, decimal and Base-n notation, divisibility, floor and ceilings, div and mod, and binomial coefficients.
