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Mathematical Thinking

Syllabus, study tools, lectures, and curriculum map.

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Weekly outline

Syllabus

Week topics from the course map

00W00

Topic

Incomplete

01W01

triangular numbers, Sigma Notation for Summation, Sequences, Peano's axioms for the natural numbers,

Incomplete

02W02

A Trip to Cantorsville, Cantor's Diagonalization Argument, Towards the Real Numbers, Ordered Field,

Incomplete

03W03

Currency Game, Divisibility, Greatest Common Divisor, The Euclidean Algorithm, Proof of the Euclidean

Incomplete

04W04

Fermat's Little Theorem, Fundamental Theorem of Arithmetic, Modular Arithmetic, Arithmetic with

Incomplete

05W05

Proof of Inclusion-Exclusion Principle, Pigeonhole Principle, Sieve of Eratosthenes, More on the

Incomplete

06W06

Binomial Coefficients, Binomial Theorem, Lattice Paths, Random Sampling, Permutations, Example

Incomplete

07W07

Graph Theory - Introduction, Connectedness and Distance in Graphs, Adjacency Matrix, Graph Trees,

Incomplete

08W08

Limit of a Sequence, Properties of Limits, Sequential Continuity, Continuity of Trigonometric

Incomplete

09W09

Limit of Fibonacci series, Lamé formula, Sandwich Lemma, Shifting Lemma

Incomplete

010W10

Derivatives, Faà di Bruno's formula

Incomplete

011W11

Riemann Integrals, Mean Value Theorem

Incomplete

012W12

Uniform continuity, Fundamental theorem of calculus

Incomplete

Study tools

Memorize first

Compact recall strip

Open notes

1 min

Advanced Proof Techniques

Open this first for the core logic and traps.

Dive in

1 min

Combinatorics and Basic Probability

Open this first for the core logic and traps.

Dive in

1 min

Common Logical Fallacies

Open this first for the core logic and traps.

Dive in

Practice Dock

One drill at a time, with Theo hints, teacher lanes, and a replay queue.

Use this when the theory is already clear and the goal is fast, clean retrieval under pressure. Mark weak questions, copy a revision pack, and move on.

TheoTeacherTextbookSpeedrun

Ask less. Recall more.

Open Practice Dock

SM-2 Active

Spaced Repetition

Flashcards

Spaced repetition engine for long-term retention of core concepts.

Start session

Not Available

Interactive Simulations

Visual Labs

Exam Mode

Adaptive Practice

Mock Exam

Set paper

Code Protocol

OPPE Simulator

Secure Comm-Link Terminal

Secure Comm-Link // Playlist Connected

Uplink 12ms

Syllabus Synchronization: Active

Open current cue

Syllabus Matrix Registry

Global Course Index

Open Full Frame

Master Registry

v6.4 Directory

Foundational

Diploma

BSc Degree

BS Degree

PG / MTech

BSMA2001

Diploma

4 Credits

Mathematical Thinking

To introduce ideas of proofs and problem solving in mathematics and to help in the transition from learning basic mathematical methods to the learn...

Deployment Hub External Docs

Execution Protocol

Module 0

Topic

Module 1

triangular numbers, Sigma Notation for Summation, Sequences, Peano's axioms for the natural numbers,

Module 2

A Trip to Cantorsville, Cantor's Diagonalization Argument, Towards the Real Numbers, Ordered Field,

Module 3

Currency Game, Divisibility, Greatest Common Divisor, The Euclidean Algorithm, Proof of the Euclidean

Module 4

Fermat's Little Theorem, Fundamental Theorem of Arithmetic, Modular Arithmetic, Arithmetic with

Module 5

Proof of Inclusion-Exclusion Principle, Pigeonhole Principle, Sieve of Eratosthenes, More on the

Module 6

Binomial Coefficients, Binomial Theorem, Lattice Paths, Random Sampling, Permutations, Example

Module 7

Graph Theory - Introduction, Connectedness and Distance in Graphs, Adjacency Matrix, Graph Trees,

Module 8

Limit of a Sequence, Properties of Limits, Sequential Continuity, Continuity of Trigonometric

Module 9

Limit of Fibonacci series, Lamé formula, Sandwich Lemma, Shifting Lemma

Module 10

Derivatives, Faà di Bruno's formula

Module 11

Riemann Integrals, Mean Value Theorem

Module 12

Syllabus

Topic

triangular numbers, Sigma Notation for Summation, Sequences, Peano's axioms for the natural numbers,

A Trip to Cantorsville, Cantor's Diagonalization Argument, Towards the Real Numbers, Ordered Field,

Currency Game, Divisibility, Greatest Common Divisor, The Euclidean Algorithm, Proof of the Euclidean

Fermat's Little Theorem, Fundamental Theorem of Arithmetic, Modular Arithmetic, Arithmetic with

Proof of Inclusion-Exclusion Principle, Pigeonhole Principle, Sieve of Eratosthenes, More on the

Binomial Coefficients, Binomial Theorem, Lattice Paths, Random Sampling, Permutations, Example

Graph Theory - Introduction, Connectedness and Distance in Graphs, Adjacency Matrix, Graph Trees,

Limit of a Sequence, Properties of Limits, Sequential Continuity, Continuity of Trigonometric

Limit of Fibonacci series, Lamé formula, Sandwich Lemma, Shifting Lemma

Derivatives, Faà di Bruno's formula

Riemann Integrals, Mean Value Theorem

Uniform continuity, Fundamental theorem of calculus

Compact recall strip

One drill at a time, with Theo hints, teacher lanes, and a replay queue.

Flashcards

Visual Labs

Mock Exam

OPPE Simulator

Secure Comm-Link Terminal

Syllabus Matrix Registry

Master Registry

Foundational

Diploma

BSc Degree

BS Degree

PG / MTech

Mathematical Thinking

Execution Protocol

Topic

triangular numbers, Sigma Notation for Summation, Sequences, Peano's axioms for the natural numbers,

A Trip to Cantorsville, Cantor's Diagonalization Argument, Towards the Real Numbers, Ordered Field,

Currency Game, Divisibility, Greatest Common Divisor, The Euclidean Algorithm, Proof of the Euclidean

Fermat's Little Theorem, Fundamental Theorem of Arithmetic, Modular Arithmetic, Arithmetic with

Proof of Inclusion-Exclusion Principle, Pigeonhole Principle, Sieve of Eratosthenes, More on the

Binomial Coefficients, Binomial Theorem, Lattice Paths, Random Sampling, Permutations, Example

Graph Theory - Introduction, Connectedness and Distance in Graphs, Adjacency Matrix, Graph Trees,

Limit of a Sequence, Properties of Limits, Sequential Continuity, Continuity of Trigonometric

Limit of Fibonacci series, Lamé formula, Sandwich Lemma, Shifting Lemma

Derivatives, Faà di Bruno's formula

Riemann Integrals, Mean Value Theorem

Uniform continuity, Fundamental theorem of calculus

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