dMAT General Academic Module Practice & Lecture Review Flashcards

Comprehensive vocabulary review flashcards covering Economics, Social Sciences, Computational Science, and General Academic Modules (dMAT Preparation).

Price Taker

A firm operating in a competitive market that cannot individually influence the market price and must accept the price determined by overall market demand and supply.

Fixed Costs

Production costs that remain constant in total regardless of the volume of output produced, such as factory rent and machinery leases.

Variable Costs

Production costs that vary directly and proportionally with the level of output, such as raw materials and hourly labor.

Break-Even Point

The production or sales output level at which total revenue exactly equals total cost, resulting in zero profit and zero loss.

Mark-Up

A pricing measure expressing the amount added to the unit cost of production as a percentage of that cost ($\text{Mark-up} = \frac{\text{Profit}}{\text{Unit Cost}}$).

Profit Margin

A pricing measure expressing profit as a percentage of the final selling price ($\text{Profit Margin} = \frac{\text{Profit}}{\text{Selling Price}}$).

Price Elasticity of Demand

A measure of the responsiveness of quantity demanded to a change in price, calculated as $\text{Elasticity} = \frac{\%\Delta Q}{\%\Delta P}$.

Elastic Demand

A condition where the percentage change in quantity demanded is greater than the percentage change in price ($|\text{Elasticity}| > 1$), causing total revenue to fall when price increases.

Inelastic Demand

A condition where the percentage change in quantity demanded is smaller than the percentage change in price ($|\text{Elasticity}| < 1$), causing total revenue to rise when price increases.

Opportunity Cost

The value of the next-best alternative option or resource use that is foregone when making a decision.

Change in Quantity Demanded

A movement along a single, fixed demand curve caused exclusively by a change in the product's own price.

Change in Demand

A shift of the entire demand curve resulting from a change in external factors other than the product's own price, such as consumer income or substitute prices.

Optimal Order Quantity ($Q^*$)

An inventory model formula ($Q^* = \sqrt{\frac{2DS}{H}}$) that minimizes the sum of fixed ordering costs and holding costs based on annual demand ($D$), order cost ($S$), and annual unit holding cost ($H$).

Deductive Research Strategy

A quantitative research approach that tests pre-formulated hypotheses and identifies causal relationships using standardized data collection and statistical analysis on representative samples.

Inductive Research Strategy

A qualitative research approach focused on discovering causal mechanisms and underlying processes through open, in-depth investigations of single or few cases.

Institutional Trust

General confidence placed in media organizations or public institutions as a whole.

Source-Specific Trust

Confidence placed in a particular, individually identified news outlet, journalist, or source.

Cross-Sectional Design

An observational research design that measures data from a population at a single point in time, making it unable to distinguish age effects from cohort effects.

Longitudinal Design

A research design that collects data from the same individual subjects repeatedly over an extended period of time.

Bonding Social Capital

Strong social ties, norms of reciprocity, and trust maintained within a relatively homogeneous social group (e.g., family or close friends).

Bridging Social Capital

Weaker social ties connecting individuals across diverse social, demographic, or cultural groups.

Ecological Fallacy

The logical error of making inferences about individual-level relationships based solely on aggregated, group-level data.

Primary Effects

Differences in educational attainment driven by prior differences in measured academic performance and achievement.

Secondary Effects

Differences in educational choices and pathways made by families of differing socioeconomic status when measured academic performance is held constant.

Residual Confounding

The persistent influence of a confounding variable that remains because the analytical control categories used were too broad or coarse.

Time Complexity

A theoretical measure describing how an algorithm's execution time or operation count grows as the input size ($n$) increases.

Big O Notation

A symbolic notation $O(f(n))$ used to express an asymptotic upper bound on the worst-case growth rate of an algorithm's resource usage.

Sorted Array

A contiguous data structure storing elements in order, allowing $O(\log n)$ binary search time but requiring $O(n)$ worst-case insertion time due to element shifting.

Hash Table

A data structure mapping keys to array slots via a hash function, providing $O(1)$ average-case time complexity for search and insertion operations.

Load Factor

The ratio of stored items to available array slots in a hash table ($\text{Load factor} = \frac{\text{items}}{\text{slots}}$).

Chaining

A hash table collision resolution technique where each slot maintains a linked list of all key-value entries that hash to the same slot index.

Recursion

A computational method where a function solves a problem by invoking smaller instances of itself until reaching a base case.

Base Case

A terminating condition in a recursive function that returns a direct value without executing any further recursive calls.

Memoisation

An optimization technique that stores the evaluation results of expensive function calls in a cache to eliminate redundant computation of overlapping subproblems.

Dynamic Programming

An algorithmic paradigm that solves complex problems by combining optimal solutions to overlapping subproblems using memoisation or tabulation.

Dijkstra's Algorithm

A graph search algorithm that computes the single-source shortest path in a graph with non-negative edge weights.

Relaxation

The step in shortest-path algorithms that updates the tentative distance to a destination vertex $B$ if a path through vertex $A$ yields a smaller total distance ($d(A) + w(A, B) < d(B)$).

Scalar Product

An algebraic operation on two vectors returning a scalar value: $\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y + a_z b_z = |\vec{a}| |\vec{b}| \cos(\varphi)$.

Vector Product

A vector operation on two 3D vectors returning a vector perpendicular to both, with magnitude $|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin(\varphi)$ equal to the area of the spanned parallelogram.

Triple Product

A vector calculation ($[\vec{a}\,\vec{b}\,\vec{c}] = \vec{a} \cdot (\vec{b} \times \vec{c})$) representing the volume of the parallelopiped spanned by three vectors; equals $0$ when vectors are coplanar.

Hydrostatic Pressure

The pressure exerted by an incompressible fluid at depth $h$, calculated as $p(h) = \rho \cdot g \cdot h + p_0$.

Buoyant Force ($F_B$)

The upward force exerted by a fluid on a submerged or floating body, equal in magnitude to the weight of the displaced fluid.

Determinant

A scalar value derived from a square matrix $A = \begin{pmatrix}a & b \\ c & d\end{pmatrix}$ as $\det(A) = a d - b c$; a matrix is invertible if and only if $\det(A) \neq 0$.

Transpose Matrix ($A^T$)

A matrix formed by interchanging the rows and columns of matrix $A$, satisfying the identity $(A \times B)^T = B^T \times A^T$.

Binomial Coefficient ($C(n,k)$)

The number of ways to choose $k$ items from $n$ distinct items without replacement and without regard to order: $C(n,k) = \frac{n!}{k!(n-k)!}$.

Half-Life ($T$)

The time required for a quantity undergoing exponential decay to decrease to half of its initial value: $N(t) = N_0 \times \left(\frac{1}{2}\right)^{t/T}$.

De Morgan's Laws

Logical rules stating that $\text{NOT}(A \text{ AND } B) = (\text{NOT } A) \text{ OR } (\text{NOT } B)$ and $\text{NOT}(A \text{ OR } B) = (\text{NOT } A) \text{ AND } (\text{NOT } B)$.

Handshake Lemma

A graph theory theorem stating that the sum of the degrees of all vertices in an undirected graph equals twice the number of edges ($\sum \text{degree}(v) = 2 E$).

Tree

A connected undirected graph with no cycles, containing exactly $n - 1$ edges for $n$ vertices.

Euler Circuit

A closed trail in a graph that visits every edge exactly once, existing if and only if the graph is connected and every vertex has an even degree.

Newton's Second Law of Motion

The fundamental principle stating that net force applied to a body equals its mass multiplied by acceleration ($F = m \cdot a$).

Newton's Third Law of Motion

The principle stating that whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first.

Boyle's Law

An ideal gas law stating that at constant temperature and gas amount, pressure and volume are inversely proportional ($p \cdot V = \text{constant}$).

First Law of Thermodynamics

The thermodynamic form of energy conservation given by $\Delta U = Q - W$, where $\Delta U$ is internal energy change, $Q$ is heat added, and $W$ is work done by the system.

Specific Heat Capacity ($c$)

The energy required to raise the temperature of $1\,\text{kg}$ of a substance by $1\,\text{K}$ ($Q = m \cdot c \cdot \Delta T$).

Le Chatelier's Principle

The principle stating that if a dynamic equilibrium is disturbed by changing conditions, the position of equilibrium shifts to counteract the disturbance.

pH Scale

A logarithmic measure of hydrogen ion concentration in solution defined by $\text{pH} = -\log_{10}[\text{H}^+]$, where a change of $1$ unit represents a 10-fold change in concentration.

Genotype

The complete genetic constitution and specific allele combination of an organism.

Phenotype

The composite observable physical or biochemical characteristics of an organism resulting from genotype-environment interactions.

Homozygous

Having two identical alleles for a particular gene (e.g., $AA$ or $aa$).

Heterozygous

Having two different alleles for a particular gene (e.g., $Aa$).

Ohm's Law

The basic electrical circuit law stating that voltage equals current multiplied by resistance ($U = R \cdot I$).

Kirchhoff's Current Law

The circuit law stating that the sum of currents entering any electrical node must equal the sum of currents leaving that node.

Kirchhoff's Voltage Law

The circuit law stating that the directed sum of potential differences (voltages) around any closed circuit loop is zero.

Mechanical Stress ($\sigma$)

Internal force per unit cross-sectional area within a deformable body, calculated as $\sigma = \frac{F}{A}$ in $\text{MPa}$ or $\text{N/mm}^2$.

Mechanical Strain ($\varepsilon$)

The dimensionless ratio of fractional length extension under load, defined as $\varepsilon = \frac{\Delta L}{L_0}$.

Hooke's Law

The elastic material relationship stating that mechanical stress is directly proportional to strain ($\sigma = E \cdot \varepsilon$).

Young's Modulus ($E$)

A mechanical material property measuring tensile stiffness in the elastic deformation regime, defined as $E = \frac{\sigma}{\varepsilon}$.

Yield Strength

The mechanical stress limit beyond which a material deforms plastically and suffers permanent shape change.

Nyquist–Shannon Sampling Theorem

The signal processing rule stating that a continuous signal can be reconstructed without aliasing only if sampled at a rate $f_s > 2 \cdot f_{\text{max}}$.

Aliasing

A signal sampling distortion where high-frequency components higher than half the sampling rate appear spuriously as lower frequencies in the sampled signal.

Quantisation Noise

The digital conversion error introduced when continuous sample amplitudes are rounded to discrete bit-depth quantisation levels.

Equity Ratio

A financial balance sheet ratio indicating capital structure and solvency, calculated as $\text{Equity Ratio} = \frac{\text{Equity}}{\text{Total Assets}}$.

Current Ratio

A financial liquidity ratio assessing short-term debt coverage, calculated as $\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$.

Asset Swap

A balance sheet transaction where one asset item increases and another asset item decreases by an equal amount, leaving total assets unchanged.

Contribution Margin per Unit

The per-unit financial contribution toward fixed costs, calculated as $\text{Unit Price} - \text{Variable Cost per Unit}$.

Fixed-Cost Degression

The economic reduction in fixed cost per unit that occurs when total fixed costs are spread over a larger production volume.

Gross Domestic Product (GDP)

The total market value of all final goods and services produced within a country's borders during a specific time period.

GDP Deflator

A broad measure of economy-wide price inflation calculated as $\text{GDP Deflator} = \frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100$.

Deflation

A sustained decrease in the general price level of goods and services across an economy.

Standard Deviation

A statistical measure of data dispersion equal to the square root of the variance, expressing scatter in the original data units.

Correlation Coefficient

A statistic bounded between $-1$ and $+1$ measuring the strength and direction of a linear relationship between two quantitative variables.

Independent Variable

The factor systematically manipulated or varied by a researcher in an experiment to observe its effect on an outcome.

Dependent Variable

The outcome variable measured in an experiment to evaluate the effect of manipulating the independent variable.

Confounding Variable

An unmeasured third variable that correlates with both the assumed cause and effect, producing a potential spurious relationship.

Reliability

The consistency and repeatability of a measurement instrument when evaluated under identical conditions.

Validity

The degree to which a research measurement instrument accurately assesses the specific construct it is intended to measure.

Phoneme

The smallest contrastive unit of sound in a language capable of distinguishing meaning between words.

Minimal Pair

A pair of words in a language that differ in meaning and sound by exactly one phoneme (e.g., 'pin' and 'bin').

Morpheme

The smallest meaningful unit of language, categorized as either free (can stand alone) or bound (must attach to a stem).

Inflection

A morphological process adding grammatical markers (such as tense or plural) to a word without changing its core word class.

Derivation

A morphological process forming a new word stem from an existing base, frequently changing the grammatical word class.

Synchronic Linguistics

The study of a language's structural state and usage at a single, specific point in time.

Diachronic Linguistics

The study of historical language evolution and structural changes occurring over time.