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Chemistry is the science of matter: what substances are made of, how they are structured, how they behave, and how they change into other substances. It sits between physics (which explains why atoms and molecules behave as they do) and biology (which depends on chemical reactions to sustain life). If you want a working definition rather than a textbook one: chemistry is the study of composition, structure, properties, and change in matter, and its main branches split by the kind of question being asked — organic, inorganic, physical, analytical, and biochemistry.

The five main branches and what each one actually does

The boundaries overlap in practice. A drug discovery team may use organic synthesis to build a molecule, physical chemistry to model how it binds, analytical chemistry to confirm its purity, and biochemistry to test it in cells. The labels describe emphasis, not sealed compartments.

How chemistry connects to everyday life and big challenges

Chemistry is not confined to laboratories. It underpins the materials in clothing and electronics, the energy stored in fuels and batteries, the medicines used in healthcare, and the processes that treat water and manage waste. The SCI (Society of Chemical Industry) frames its work around exactly these intersections — its stated themes include agrifood, energy, health and wellbeing, materials, and sustainability and environment, and it describes itself as a global network of innovators using science to tackle societal challenges across climate and planet and health and wellness.

Two examples from SCI's own coverage illustrate the range:

• Textile circularity. SCI notes that people are buying more clothes but wearing them less before disposal, and textile waste has continued to increase over the past five to ten years. Chemistry contributes here through fibre recycling, dye removal, and new material design.
• Geothermal energy. According to SCI, the International Energy Agency projected in late 2024 that geothermal energy could supply as much as 15% of global electricity demand between now and 2050 — a sharp revision from two years earlier, when its share was expected to stay near 1%. Chemistry and materials science matter for drilling fluids, heat-exchange materials, and corrosion control in these systems.

These are examples of how the discipline is applied, not a complete list of its relevance.

How to learn more or get involved

If you want to go further, the practical routes depend on where you are starting:

• Students or early-career scientists: look for degree programmes that cover the five branches above, then specialise. SCI runs a College of Scholars, a mentoring programme, and Bright SCIdea (an entrepreneurship competition), which are aimed at people building a career in science-related fields.
• Professionals in industry or academia: SCI's Interest Groups organise around themes such as agrifood, energy, health and wellbeing, materials, and sustainability and environment. These groups host events and enable networking and collaborations.
• General readers: SCI publishes news, a media centre, C&I (Chemistry & Industry), journals, an SCIblog, and videos. These are accessible entry points for following current developments without a formal background.
• Anyone considering membership: SCI offers member sign-in and sign-up, and a "Become a Member" route. It also lists awards, medals, memorial lectures, honours, scholarships and fellowships, travel bursaries, and prizes. The site includes a newsletter subscribe link; specific pricing or access terms are not stated in the material available here, so check the membership page directly before assuming cost or eligibility.

A reasonable next step is to pick one branch that matches your interest — for example, materials chemistry if you care about sustainability, or biochemistry if health is your focus — and follow the relevant SCI interest group or publication rather than trying to cover all five at once.

Precalculus is the course that sits between algebra/trigonometry and calculus. It reviews and extends the algebra and trig you already know, then adds the specific tools calculus depends on: a deep understanding of functions, their graphs, and the idea of a limit. You typically take it in your last year of high school or first year of college if you plan to study calculus, engineering, physics, or another quantitative field. The expected background is solid algebra (solving equations, working with exponents) and basic trigonometry.

What Precalculus Actually Is

Precalculus is not one new subject. It is a consolidation course. Its job is to make sure you can manipulate and interpret the functions that calculus will ask you to differentiate and integrate. If algebra teaches you to solve for x, precalculus teaches you to think about f(x) as an object — how it behaves, what its graph looks like, and how it changes.

That shift matters because calculus is built on two questions: how fast does something change, and how much accumulates. Both questions are asked about functions. Precalculus is where you get fluent with those functions before the speed and accumulation machinery arrives.

Core Topics Precalculus Covers

The exact syllabus varies by school, but most precalculus courses cover the following. Video-Tutor.net lists precalculus as one of its main course categories alongside algebra, trigonometry, and calculus, which reflects this same sequence.

Functions and Their Graphs

• Definition of a function, domain and range, function notation
• Transformations: shifts, stretches, reflections
• Composition and inverse functions
• Piecewise functions

This is the backbone of the whole course. Every later topic is a specific type of function.

Polynomial and Rational Functions

• Linear, quadratic, and higher-degree polynomials
• End behavior, zeros, and multiplicity
• Rational functions, asymptotes (vertical, horizontal, slant)
• Polynomial and rational inequalities

Exponential and Logarithmic Functions

• Exponential growth and decay
• Logarithm laws and solving exponential/log equations
• The natural base e

These show up constantly in calculus, especially in derivative and integral rules.

Trigonometry

• The unit circle, radians, and trig functions of any angle
• Graphs of sine, cosine, tangent and their transformations
• Inverse trig functions
• Trigonometric identities and equations
• Law of Sines and Law of Cosines

Trig is often taught as its own course and then folded into precalculus. Either way, calculus of trig functions assumes you already know these cold.

Sequences, Series, and Limits

• Arithmetic and geometric sequences
• Summation notation and series
• An introduction to limits and continuity

The limits section is the bridge to calculus. It is where precalculus stops being review and starts previewing the next course.

How Each Topic Prepares You for Calculus

The pattern is consistent: precalculus gives you the objects, calculus gives you the operations on them. Skip the precalculus fluency and the calculus rules feel like arbitrary memorization.

Who Takes Precalculus and What You Need First

Precalculus is standard for:

• High school students on a math track toward calculus (usually juniors or seniors)
• College students who need calculus for a STEM, business, or health-science major but whose placement test did not clear them for calculus
• Anyone returning to math after a gap who needs to rebuild algebra and trig before calculus

You should be comfortable with: solving linear and quadratic equations, factoring, exponent rules, simplifying fractions with variables, and the basics of right-triangle trigonometry. If those are shaky, expect to spend extra time on the early function chapters.

How to Study Precalculus

Because the course is broad, the most common failure mode is falling behind on one topic and having it resurface later. A few practical approaches:

1. Work topic by topic, not chapter by chapter. Master functions before moving to rational functions; master trig before limits.
2. Graph everything. Sketching by hand builds the intuition that calculus depends on.
3. Do problems without looking at solutions first. Precalculus rewards repetition more than reading.
4. Use video lessons to reinforce a specific topic. Video-Tutor.net organizes its content by course — algebra, trigonometry, precalculus, calculus, and others — so you can find lessons matched to the topic you are stuck on rather than watching a full course in order. It also lists formula sheets and video playlists, which are useful for review before a test.

If you are choosing between self-study and a class, the deciding factor is usually whether you can stay disciplined across a wide syllabus. Precalculus is not conceptually hard at any single point, but it is long, and gaps compound.

Calculus is the branch of mathematics that studies two connected ideas: how quantities change (rates of change) and how small changes accumulate into a total (accumulation). It splits into two main branches — differential calculus and integral calculus — and both rest on the concept of a limit. You typically study it after algebra, trigonometry, and precalculus, and it is a standard requirement for physics, engineering, economics, and many other quantitative fields. Video-Tutor.net lists calculus as one of its course topics alongside algebra, trigonometry, precalculus, chemistry, physics, organic chemistry, and statistics, which reflects that sequencing.

The Two Core Questions of Calculus

The two branches are linked by the Fundamental Theorem of Calculus, which shows that differentiation and integration are inverse processes. That link is why a single course covers both.

Key Foundational Concepts

• Limits — the value a function approaches as the input approaches some point. Limits are the foundation for both derivatives and integrals.
• Derivatives — the instantaneous rate of change of a function, interpreted geometrically as the slope of the tangent line.
• Integrals — accumulation, interpreted geometrically as area under a curve (definite integral) or as a family of antiderivatives (indefinite integral).
• Continuity — a property that determines whether limits and derivatives behave as expected at a point.

Common Topics in an Introductory Calculus Course

Differential calculus topics

• Computing limits, including one-sided limits and limits at infinity
• Definition of the derivative and its interpretation as a rate of change
• Differentiation rules: power, product, quotient, and chain rules
• Derivatives of trigonometric, exponential, and logarithmic functions
• Implicit differentiation and related rates
• Finding maxima and minima, and curve sketching
• The Mean Value Theorem and its applications

Integral calculus topics

• Antiderivatives and the indefinite integral
• Riemann sums and the definite integral
• The Fundamental Theorem of Calculus
• Basic integration techniques such as substitution
• Area between curves
• Volumes of solids of revolution
• An introduction to sequences and series in many courses

Where Calculus Is Used

• Physics — velocity and acceleration are derivatives of position; work and displacement involve integrals.
• Engineering — modeling changing systems such as circuits, fluid flow, and structural stress.
• Economics — marginal cost and marginal revenue are derivatives; total accumulation over time uses integrals.
• Statistics — continuous probability distributions rely on integration.
• Computer graphics and machine learning — gradients (multivariable derivatives) drive optimization.

How Calculus Connects to Earlier Courses

Algebra supplies the manipulation skills for solving equations and simplifying expressions. Trigonometry provides the function identities needed to differentiate and integrate trigonometric functions. Precalculus introduces functions, their graphs, and the limit idea informally, which is why it is normally the direct prerequisite. Video-Tutor.net groups calculus with precalculus, trigonometry, and algebra as separate course listings, matching this progression.

How to Approach Learning It

1. Confirm your prerequisites: solid algebra and trigonometry, plus familiarity with functions and graphs.
2. Start with limits before derivatives — the derivative is defined as a limit, so skipping this step causes problems later.
3. Practice differentiation rules until they are automatic, then move to applications such as optimization and related rates.
4. Learn integration as the reverse process, then apply it to area and volume problems.
5. Use worked examples and practice problems to check each step, since calculus errors are usually algebraic rather than conceptual.

A common sticking point is treating the derivative as a formula to memorize rather than a rate of change to interpret; another is underestimating how much algebra and trigonometry fluency the course assumes. If either feels shaky, review those topics first.

Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles, especially right triangles. It gives you a set of functions—sine, cosine, tangent, and their reciprocals—that connect an angle to a ratio of two sides. Those functions extend beyond triangles through the unit circle, which lets you work with any angle, not just the acute angles inside a right triangle. If you are starting from scratch, the practical path is: learn the six functions, understand the unit circle, memorize the core identities, then practice solving for missing sides and angles.

The six trigonometric functions

Every right triangle has three sides relative to a chosen angle: the hypotenuse (opposite the right angle), the opposite side (across from the angle), and the adjacent side (next to the angle). The six functions are just different pairings of those sides.

The last three are reciprocals of the first three: csc is 1/sin, sec is 1/cos, and cot is 1/tan. That means if you know sine, cosine, and tangent, you can derive the other three without memorizing new ratios.

A common memory aid for the first three is SOH-CAH-TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

The unit circle: extending trig to any angle

Right-triangle ratios only work for angles between 0° and 90°. The unit circle—a circle of radius 1 centered at the origin—removes that limit.

On the unit circle, an angle is measured from the positive x-axis, and the point where the angle's ray hits the circle has coordinates (cos θ, sin θ). This definition works for any angle, including angles larger than 90° and negative angles, and it produces the signs you see in each quadrant:

• Quadrant I (0°–90°): sin, cos, tan all positive
• Quadrant II (90°–180°): sin positive, cos and tan negative
• Quadrant III (180°–270°): tan positive, sin and cos negative
• Quadrant IV (270°–360°): cos positive, sin and tan negative

The unit circle also gives you the exact values for common angles (30°, 45°, 60°, and their multiples), which is why it is usually the second thing you study after the basic ratios.

Core identities and formulas

Identities are equations that hold for every angle. The ones you use most:

• Pythagorean identity: sin²θ + cos²θ = 1. This follows directly from the unit circle and the Pythagorean theorem.
• Reciprocal identities: csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.
• Quotient identity: tan θ = sin θ / cos θ.
• Complementary angles: sin(90° − θ) = cos θ, and tan(90° − θ) = cot θ.

These are used to simplify expressions, prove other identities, and rewrite an equation into a form you can solve. For example, if an equation contains sin²θ, substituting 1 − cos²θ often turns it into something solvable for cos θ.

Solving for a missing side or angle

This is the skill most courses test first. The steps:

1. Label the triangle. Identify the right angle, then mark the side opposite your known or target angle, the adjacent side, and the hypotenuse.
2. Choose a function. Pick the one that relates the two sides you care about. If you know the opposite and hypotenuse, use sine. If you know the adjacent and hypotenuse, use cosine. If you know opposite and adjacent, use tangent.
3. Set up the equation. For a missing side, write the ratio equal to the known values and solve. For a missing angle, take the inverse function (sin⁻¹, cos⁻¹, or tan⁻¹) of the ratio.
4. Check the result. A side must be shorter than the hypotenuse, and an angle must fall in a range consistent with the triangle's shape.

Example: A right triangle has a 35° angle and a hypotenuse of 12. To find the side opposite the 35° angle, use sine: sin 35° = opposite / 12, so opposite = 12 × sin 35° ≈ 6.88. The answer is less than 12, which checks out.

For non-right triangles, you switch to the law of sines (a/sin A = b/sin B = c/sin C) or the law of cosines (c² = a² + b² − 2ab cos C). These come up after the right-triangle material.

How to learn it step by step

Trigonometry builds on itself, so the order matters more than the pace. A workable sequence:

1. Angle measurement in degrees and radians
2. The six functions and SOH-CAH-TOA
3. Special right triangles (30-60-90 and 45-45-90)
4. The unit circle and reference angles
5. Graphing sine, cosine, and tangent
6. Identities and how to verify them
7. Solving triangles with the law of sines and law of cosines

Video-Tutor.net lists trigonometry as a dedicated course alongside algebra, precalculus, and calculus, and organizes its material into course videos, video playlists, and formula sheets. That structure fits this sequence: use the formula sheets as a reference while working problems, and the playlists to move through topics in order. The site also separates test-prep and final-exam videos, which are useful once you have covered the core material and want to check retention.

If you are deciding where to start, the honest test is whether you can already solve a right triangle for a missing side using sine, cosine, or tangent. If not, begin there before touching the unit circle or identities—those depend on it.

Physics is the study of matter, energy, force, and motion—how the universe behaves at scales from subatomic particles to galaxies. You can follow current physics research by reading department news pages, colloquium announcements, and public science feeds, and by learning to tell observation, experiment, and theory apart. This guide explains what the field covers and how to read physics news without overinterpreting it.

What physics actually studies

Physics looks for the basic rules that govern how things move and interact. That includes:

• Mechanics — motion, forces, momentum, and energy, from falling objects to orbital dynamics.
• Electromagnetism — electric and magnetic fields, light, and radiation.
• Thermodynamics and statistical mechanics — heat, entropy, and how large collections of particles behave.
• Quantum mechanics — behavior at atomic and subatomic scales, where particles also behave like waves.
• Relativity — space, time, and gravity at high speeds and large masses.
• Astrophysics and astronomy — applying physics to stars, planets, and the cosmos.

Adjacent fields overlap heavily. Acoustics, for example, is applied mechanics and wave physics: it studies how sound is generated, travels, and affects structures, people, and wildlife. Astronomy is often treated as a separate department but rests on the same physical laws.

A common misconception is that physics is only math or only cosmology. In practice it spans tabletop experiments, engineering-adjacent measurement work, and observational astronomy.

How to read a physics research news item

Physics news mixes several kinds of claims. Sorting them helps you judge what is actually being reported.

For example, a photo showing the Sun with silhouettes of both the International Space Station and an airplane is an observation—a planned, sub-second exposure. The photographer's estimate that such an alignment is about 30 million to one is a statistical claim about that specific image, not a physical law. Reading it as "physics proves rare alignments" would be a misread.

Where to find physics talks, papers, and public resources

University department sites are a practical entry point. A typical physics and astronomy department page collects:

• Colloquium and seminar listings — scheduled talks, often open online, with titles and abstracts.
• Selected publications — recent papers by faculty and students.
• News and events — awards, outreach, and department updates.
• Public science feeds — for astronomy, NASA's APOD (Astronomy Picture of the Day) is a widely used daily image with an explanation.

When you open a colloquium listing, the abstract usually states the question, the method, and why it matters. That structure is a good template for reading any physics talk or paper summary.

Common pitfalls when following physics news

• Treating a model as settled fact. A theory that fits data is not the same as a confirmed mechanism.
• Ignoring scale and uncertainty. Numbers in physics come with error ranges and conditions.
• Assuming physics equals astronomy. Acoustics, materials, and quantum information are just as central.
• Skipping the method. The "how" often determines how much a result can be trusted.

If you want a reliable routine: pick one department news page and one public feed, read the abstract or caption first, then check whether the claim is an observation, an experiment, or a theory. That habit will let you follow physics research without needing a specialist background.