A structured curriculum for someone with strong mathematics and physics preparation who wants genuine undergraduate-level competence in chemistry, starting from zero.
The advantage of coming from pure math and physics: you already have the calculus, linear algebra, differential equations, and quantum mechanics intuition that most chemistry students struggle with. Physical chemistry will feel natural. The challenge: chemistry has a large empirical and descriptive component that cannot be derived from first principles. You have to learn facts, memorize patterns, and develop chemical intuition through exposure. Do not resist this. It is not intellectual weakness; it is the nature of the subject.
This is the equivalent of a two-semester freshman sequence. It covers the core vocabulary and conceptual framework of the entire discipline.
Atkins, Jones, and Laverman -- Chemical Principles: The Quest for Insight (8th edition or later)
This is the rigorous general chemistry text. It assumes comfort with algebra and basic calculus and does not waste time on hand-holding. The thermodynamics and quantum chapters are written by Peter Atkins, who is the best expository writer in physical chemistry.
If unavailable, the fallback is:
Zumdahl and Zumdahl -- Chemistry (10th edition or later)
More thorough on stoichiometry and equilibrium calculations. Slightly less elegant than Atkins but covers everything you need with excellent worked examples.
Atomic structure and periodicity. Electron configurations, quantum numbers, orbital shapes, periodic trends (ionization energy, electron affinity, electronegativity, atomic radius). You already know the hydrogen atom from physics -- chemistry extends this to multi-electron atoms via shielding and effective nuclear charge.
Chemical bonding. Ionic vs. covalent, Lewis structures, VSEPR theory, molecular geometry, hybridization, molecular orbital theory. MO theory will feel natural given your linear algebra background.
Stoichiometry. Mole concept, balancing equations, limiting reagents, percent yield. Not deep but you must be fluent.
States of matter and intermolecular forces. Gas laws, kinetic molecular theory, phase diagrams, London dispersion, dipole-dipole, hydrogen bonding.
Solutions and colligative properties. Concentration units, solubility, Raoult's law, boiling point elevation, freezing point depression, osmotic pressure.
Chemical thermodynamics. Enthalpy, entropy, Gibbs free energy, Hess's law, standard formation enthalpies. You know thermodynamics from physics; here you learn to predict whether reactions actually happen.
Chemical kinetics. Rate laws, reaction order, Arrhenius equation, collision theory, transition state theory, catalysis. Differential equations applied to reaction rates.
Chemical equilibrium. Equilibrium constants, Le Chatelier's principle, ICE tables, reaction quotients.
Acid-base chemistry. Bronsted-Lowry theory, pH, pKa, buffer solutions, titration curves, polyprotic acids. Master this thoroughly; it returns everywhere in organic and biochemistry.
Electrochemistry. Galvanic and electrolytic cells, standard reduction potentials, Nernst equation, Faraday's laws.
Nuclear chemistry. Radioactive decay, half-lives, binding energy, fission, fusion.
Do the harder end-of-chapter problems from the textbook. Chemistry is learned by solving problems, same as mathematics. Aim for at least 10-15 problems per topic.
Organic chemistry is the largest body of knowledge in this curriculum. The difficulty is not mathematical -- it is pattern recognition and spatial reasoning. You are learning a language of molecular transformations. There are roughly 60-80 named reactions you need to internalize.
Clayden, Greeves, Warren, and Wothers -- Organic Chemistry (2nd edition, 2012)
The best organic chemistry textbook written in the last thirty years. It teaches organic chemistry as a logical system of reactivity principles rather than a catalog of reactions to memorize. The mechanism-first approach means you learn WHY reactions happen, not just WHAT happens. Used at Oxford, Cambridge, and most serious UK chemistry programs.
Clayden is 1500 pages. Read it linearly. Do the in-chapter exercises.
Do not use McMurry, Bruice, or Wade as your primary text. They are written for pre-med students and organize material around functional groups rather than mechanistic principles.
Structure and bonding review. Hybridization, electronegativity, resonance, inductive effects. Clayden chapters 1-3.
Functional groups and nomenclature. Alkanes, alkenes, alkynes, alcohols, ethers, aldehydes, ketones, carboxylic acids, esters, amines, amides.
Stereochemistry. Chirality, enantiomers, diastereomers, R/S configuration, E/Z notation, optical activity, meso compounds. Use a physical model kit or 3D visualization tool.
Reaction mechanisms: nucleophilic substitution and elimination. SN1, SN2, E1, E2. These four mechanisms and the factors that control competition between them are the foundation of organic reactivity.
Addition reactions to alkenes and alkynes. Electrophilic addition, Markovnikov's rule, hydroboration, catalytic hydrogenation, epoxidation.
Carbonyl chemistry. Nucleophilic addition to aldehydes and ketones, acyl substitution at carboxylic acid derivatives. The core of organic chemistry. Clayden treats this brilliantly.
Enolate chemistry. Aldol reactions, Claisen condensation, Michael addition, enamine chemistry. Where synthesis planning begins.
Aromatic chemistry. Aromaticity, electrophilic aromatic substitution, nucleophilic aromatic substitution, directing effects. Huckel's rule connects to MO theory.
Pericyclic reactions. Diels-Alder, electrocyclic reactions, sigmatropic rearrangements, Woodward-Hoffmann rules. Where your math background pays off -- these reactions are controlled by orbital symmetry.
Retrosynthetic analysis. Disconnection approach, synthons, functional group interconversions. Strategic thinking: given a target molecule, plan a synthetic route backwards.
You cannot derive organic chemistry from first principles. There are patterns and principles, but ultimately you need to know that LiAlH4 reduces esters to alcohols while DIBAL-H reduces them to aldehydes. Flashcards (Anki) for reaction conditions and reagents are not beneath you.
This is your home territory. Physical chemistry is applied mathematics and physics to chemical systems.
McQuarrie and Simon -- Physical Chemistry: A Molecular Approach (1997)
The definitive physical chemistry textbook for someone with your background. Quantum mechanics first, then statistical thermodynamics, then chemical applications. Mathematically rigorous without being pedantic. The problems are excellent.
Most chemistry programs use Atkins' Physical Chemistry (the "big Atkins"), which covers similar material but in a different order (thermodynamics first). McQuarrie is better for someone coming from physics.
Atkins and de Paula -- Physical Chemistry (11th edition or later)
Use as a reference for broader coverage of applied topics (electrochemistry, transport properties, surface chemistry).
Quantum Chemistry (your strongest area)
Postulates of quantum mechanics, Schrodinger equation, particle in a box, harmonic oscillator, rigid rotor. You know all of this. The chemistry version emphasizes applications to molecular systems.
Hydrogen atom and multi-electron atoms. Variational principle, perturbation theory, Hartree-Fock. Learn the chemistry applications (term symbols, selection rules).
Molecular orbital theory. LCAO-MO, Huckel theory, Walsh diagrams, computational chemistry overview. Huckel theory is linear algebra applied to conjugated pi systems.
Molecular spectroscopy. Rotational, vibrational, electronic spectroscopy. Selection rules from group theory. UV-vis, IR, NMR theory.
Group theory and symmetry. Point groups, character tables, symmetry-adapted linear combinations, selection rules derived from symmetry. Abstract algebra applied to molecular symmetry.
Statistical Thermodynamics
Boltzmann distribution, partition functions, connection to thermodynamic quantities. Deriving thermodynamics from statistical mechanics with chemical applications.
Ideal gas partition function, internal energy, heat capacity, entropy of mixing. Chemical equilibrium derived from partition functions.
Einstein and Debye models of solids.
Chemical Kinetics (mathematical treatment)
Rate laws as differential equations, integrated rate laws, steady-state approximation, Lindemann mechanism, transition state theory, Eyring equation.
Reaction dynamics. Potential energy surfaces, molecular beam experiments, Marcus theory of electron transfer.
Transition metals, coordination compounds, organometallics, solid state chemistry, bioinorganic chemistry. More descriptive than organic or physical chemistry, but the theoretical underpinnings (group theory, crystal field theory, MO theory for metal complexes) will appeal to your mathematical sensibility.
Housecroft and Sharpe -- Inorganic Chemistry (5th edition or later)
The standard comprehensive inorganic text worldwide. Covers everything from main group descriptive chemistry to advanced topics in catalysis and materials science.
Main group chemistry. Systematic treatment of Groups 1-2, 13-18. Descriptive but important: you need to know what elements actually do.
Coordination chemistry. Werner's theory, nomenclature, isomerism in octahedral and square planar complexes, chelate effect, thermodynamic and kinetic stability.
Crystal field theory and ligand field theory. d-orbital splitting, spectrochemical series, crystal field stabilization energy, magnetism, color. CFT is electrostatic; LFT adds MO theory. Both are elegant and predictive.
Electronic spectra of transition metal complexes. Term symbols, Tanabe-Sugano diagrams, selection rules, charge transfer bands. Group theory is essential here.
Organometallic chemistry. Metal carbonyls, metallocenes, 18-electron rule, oxidative addition, reductive elimination, insertion, beta-hydride elimination. Catalytic cycles (hydrogenation, cross-coupling, olefin metathesis).
Solid state chemistry. Crystal structures, band theory, semiconductors, superconductors. Band theory is Bloch's theorem applied to infinite lattices.
Bioinorganic chemistry. Metalloenzymes, oxygen transport (hemoglobin/myoglobin), electron transfer proteins, photosynthesis, nitrogen fixation.
You do not need a full analytical chemistry course, but you need to understand the major techniques and what information they provide.
Harris -- Quantitative Chemical Analysis (10th edition or later)
Focus on these areas:
Statistics of measurement. Error analysis, significant figures, confidence intervals, propagation of uncertainty.
Gravimetric and volumetric analysis. Titrations (acid-base, redox, complexometric), precipitation methods.
Spectroscopic methods. UV-vis spectroscopy (Beer-Lambert law), atomic absorption/emission, mass spectrometry, NMR spectroscopy (chemical shift, coupling, integration -- the most important analytical technique in organic chemistry).
Chromatography. Gas chromatography, HPLC, thin-layer chromatography. Separation principles.
Electroanalytical methods. Potentiometry, voltammetry, coulometry.
Pavia, Lampman, Kriz, and Vyvyan -- Introduction to Spectroscopy (5th edition)
The standard text for learning to interpret NMR, IR, and mass spectra. Work through the NMR and IR chapters and practice the spectral identification problems. This skill is essential for organic chemistry.
The goal is to understand the chemical logic of biological systems.
Voet and Voet -- Biochemistry (4th edition)
The rigorous biochemistry text. Assumes organic chemistry, does not shy away from thermodynamics and kinetics. Better than Lehninger for someone with your quantitative background.
If too heavy for an overview:
Berg, Tymoczko, Gatto, and Stryer -- Biochemistry (9th edition)
Slightly more accessible, still serious.
Amino acids and protein structure. Primary, secondary, tertiary, quaternary structure. Ramachandran plots. Protein folding.
Enzyme kinetics. Michaelis-Menten kinetics, Lineweaver-Burk plots, inhibition (competitive, uncompetitive, noncompetitive). Differential equations applied to biological catalysis.
Enzyme mechanisms. Serine proteases, lysozyme, carbonic anhydrase. Organic reaction mechanisms in biological contexts.
Metabolism overview. Glycolysis, citric acid cycle, oxidative phosphorylation, fatty acid oxidation, gluconeogenesis. Follow the thermodynamic logic.
Nucleic acid chemistry. DNA and RNA structure, base pairing, replication, transcription, translation (overview).
Lipids and membranes. Membrane structure, transport, signal transduction (overview).
Zubrick -- The Organic Chem Lab Survival Manual (11th edition)
A short, readable guide to common lab techniques: distillation, extraction, recrystallization, chromatography, reflux, rotary evaporation. Read it once in a weekend.
Time estimate. At 10-15 hours per week, this curriculum takes 12-14 months. Phases 3 and 2 can partially overlap since they use different cognitive skills.
What to skip if time-limited. Analytical chemistry can be reduced to NMR and mass spectrometry only. Biochemistry can be reduced to enzyme kinetics and metabolism. Do not skip general, organic, or physical chemistry.
Where your math background helps most. Physical chemistry, thermodynamics, kinetics, MO theory, group theory applications, enzyme kinetics.
Where your math background does not help. Descriptive inorganic chemistry, organic reaction memorization, functional group chemistry, nomenclature. These require raw exposure and repetition.
A note on rigor. Chemistry is an experimental science. Theories in chemistry are models that work within domains of validity, not deductive systems. VSEPR is empirically useful despite having no rigorous theoretical justification. Crystal field theory is "wrong" (it ignores covalency) but predictive. If you expect mathematical rigor at every step, you will be frustrated. The rigor in chemistry is in experimental methodology and in physical chemistry; the rest is principled pragmatism.