How-to library
Method pages, one routine each: how to complete the square, how to integrate by parts, how to balance a redox equation. Every page runs a full worked example.
Number Theory
How to write a proof by inductionLearn the standard steps to write a mathematical proof by induction, including the base case and inductive step.
Number Theory
How to solve a modular arithmetic equationLearn how to solve linear congruences using the greatest common divisor and modular multiplicative inverses.
Number Theory
How to count with the inclusion-exclusion principleLearn how to use the inclusion-exclusion principle to compute the cardinality of the union of multiple overlapping sets in discrete mathematics.
Economics
How to calculate GDP with the expenditure approachCalculate Gross Domestic Product by summing consumption, investment, government spending, and net exports using the standard expenditure equation.
Number Theory
How to find the GCD with the Euclidean algorithmLearn to compute the greatest common divisor of two integers using the Euclidean algorithm by applying repeated division and remainder substitution.
Economics
How to calculate consumer and producer surplusCalculate consumer and producer surplus by finding market equilibrium and computing the areas between the price level and the demand or supply curves.
Economics
How to find market equilibrium from supply and demand equationsCalculate market equilibrium price and quantity by setting the algebraic supply and demand equations equal to each other.
Economics
How to calculate price elasticity of demandCalculate the price elasticity of demand using the midpoint method to determine quantity responsiveness to price changes.
Accounting
How to calculate straight-line depreciationLearn how to calculate straight-line depreciation by dividing the depreciable base of an asset by its useful life.
Accounting
How to calculate cost of goods soldA step-by-step method to calculate Cost of Goods Sold (COGS) using beginning inventory, purchases, and ending inventory.
Accounting
How to prepare a trial balanceLearn how to prepare a trial balance by listing all ledger accounts and ensuring total debits equal total credits.
Accounting
How to record a journal entryLearn how to identify affected accounts, apply debit and credit rules, and record standard accounting journal entries.
Finance
How to compute break-even quantityCompute the break-even quantity by dividing total fixed costs by the contribution margin per unit.
Finance
How to calculate net present value of a projectCalculate the net present value (NPV) by discounting all future cash flows to the present using a specified discount rate and subtracting initial costs.
Finance
How to calculate a loan paymentA direct method to calculate fixed periodic loan payments using the time value of money present value annuity formula.
Finance
How to calculate the present value of an annuityCalculate the present value of an ordinary annuity by discounting equal, periodic cash flows at a constant interest rate.
Finance
How to calculate compound interestLearn how to calculate compound interest using the standard formula, including the setup, step-by-step procedure, and common errors to avoid.
Computer Science
How to evaluate a postfix expression with a stackEvaluate postfix expressions in Reverse Polish Notation systematically using a stack data structure in linear time.
Computer Science
How to reverse a linked listLearn how to reverse a singly linked list in-place using iterative pointer manipulation in time complexity O(n).
Computer Science
How to insert into a binary search treeA precise procedure for inserting a new node into a binary search tree while maintaining the binary search tree property.
Computer Science
How to simplify a Boolean expression with a Karnaugh mapMinimize Boolean expressions using Karnaugh maps by grouping adjacent 1s to find the simplest sum-of-products form.
Computer Science
How to convert a decimal number to binary and hexadecimalA step-by-step method for converting base-10 decimal numbers into base-2 binary and base-16 hexadecimal using repeated division.
Computer Science
How to perform binary search on a sorted arrayLearn how to perform binary search on a sorted array to find a target element in O(log n) time.
Computer Science
How to trace a recursive function by handLearn how to manually trace a recursive function using a call stack diagram to systematically track variables, state, and return values.